Warmup 8-17(Geom) Add or subtract each set of polynomials. Answers should be in standard form. Show work! 1. (16x - 7x3 + 13) - (19x3 + 23 - 41x) Multiply the polynomials below. Show work! 2. (3x - 2)(4x2 – 5x - 1) Use the rules of exponents to simplify the following expressions. 3. (5x3y2)(-9x5y-4) 4. (-3x-3y4)-2

Examples of Rational/Irrational #’s, Perfect Squares and Factors(Geom) Identify whether each number below is rational or irrational. 1. ½ 2. √5 3. √16 -1/3 5. 6.825 6. π √12 8. 1 +√80 9. 3√8 What makes a number a perfect square? Why is the word “square” used? Determine the perfect square values for the integers 0-15. List all factors for the following numbers: 28 2. 32 3. 60 72 5. 84 6. 100 Make a factor tree for the following numbers: 40 2. 56 3. 80 4. 96 5. 120

Rational vs. Irrational #’s, Perfect Squares and Factor Practice(Geom) Identify whether each number below is rational or irrational. Explain. 1. √11 2. 3π 3. √81 4. -4/5 5. .8125 6. 5 + √121 7. π/4 8. 4 +√6 9. 8√12 10. 7√25 Determine if the following numbers are perfect squares. Show why. 144 12. 288 13. 48 14. 324 15. 900 16. 120 Make a factor tree for the following numbers: 17. 45 18. 60 19. 88 80 21. 96 22. 100 23. 150 24. 144

Ticket out the Door 8-17(Geom) Identify whether each number below is rational or irrational. Explain. 1. 14 -√121 2. π/6 3. 7√5 4. 1.0025 Determine if the following numbers are perfect squares. Show why. 5. 169 6. 80 Make a factor tree for the following numbers: 7. 54 8. 64

Warmup 8-19(Geom) Add or subtract the polynomials below. Show work! 1. (13x3 – 4x4 + 9x2) – (11x2 – 19x4 + 7x) Use the rules of exponents to simplify the following expressions. 2. -18x-4y6 3. (5x2y-3)2 45xy2 4. Tell whether the following expressions are examples of rational or irrational numbers. 11π b. 2 + √49

Warmup 8-24(Geom) 1. (-5x9y-7)(9x-5y-2) 5√144 b. 9 + √37 Use the rules of exponents to simplify the following expressions. 1. (-5x9y-7)(9x-5y-2) 2. Tell whether the following expressions are examples of rational or irrational numbers. 5√144 b. 9 + √37 Simplify: √(90x2y) Add or subtract: √80 - 3√48 + 2√75 - 4√125

Use the rules of exponents to simplify the Warmup 8-21(Geom) Use the rules of exponents to simplify the following expressions. No negative exponents in the answers. 1. (6x-3y4)(-11x7y-8) 2. -20x5y-3 28x-4y-1 3. Simplify: √(64x3y4) 4. Tell whether the following expressions are examples of rational or irrational numbers. 5√144 b. 9 + √37

2. 25x-7y-5 30x4y-9 3. (2x-4y8)5 4. Simplify: √(60x6y3) Warmup 8-25(Geom) Use the rules of exponents to simplify the following expressions. No negative exponents in the answers. 1. (8x5y-3)(-6x-2y-7) 2. 25x-7y-5 30x4y-9 3. (2x-4y8)5 4. Simplify: √(60x6y3)

Tell whether the following expressions are examples of rational or Geometry Mini Quiz Rationals, Irrationals, Radicals, and Exponent Rules Tell whether the following expressions are examples of rational or irrational numbers. 1. 11 - 2π 2. 7√25 Simplify each radical expression below. Show work! 3. √(28xy2) 4. √(49x4y6.) 5. √(96xy3) Combine like terms in the following radical expressions. Show work! 6. 2√96 - √90 - 3√40 7. 4√28 - 5√44 + √63 + 2√99 Use exponent rules to simplify the following expressions. No negative exponents! 8. (-5x9y-7)(9x-5y-2) 9. (3x-4y6)5 10. -14x-3y4 11. (-5) -7 × (-5) 4 20x-8y-2

Examples Greatest Common Factor 8-21(Geom) Factor the GCF out of each polynomial. Show work! 1. 6x – 48 2. 14x3 – 39x2 3. 16x2 – 24x – 40 4. 10x2y + 25xy2 – 30x3 5. 27x2y2 + 9xy - 36x2y3 6. 36x3y2 – 60x2y2 - 24x2y

Ticket Out the Door 8-24(geom.) (Greatest Common Factor) Factor the GCF out of each polynomial. Show work! 18x2 – 27x + 45 32x2y + 56xy2 – 16y3 35x3y2 – 7xy + 63x2y3 24x2y3 – 15x2y2 + 10x2y

Warmup 8-27 Add or Subtract: 3√(80) - 2√(72) - √(125) - 4√(50) Factor the GCF out of each polynomial. Show work! 2. 32x3y - 40x2y2 3. 27x2y - 9xy2 - 54x2y2

Warmup 8-28 Factor the following equations completely. Show work! x2 – 8x - 84 x2 - 18x + 81 15x3y2 – 36x2y 4. 6x2 - 12x - 90

Ticket Out the Door 8-28 Factoring A>1, with GCF Factor the following equations completely. Show work! 2x2 – 6x – 9 2. 5x2 – 14x + 8 6x2 + 33x + 42 4. 3x2 + 9x – 10

Warmup 8-31 Factor the following equations completely. Show work! x2 – 14x - 95 24x2y + 6xy – 30y2 5x2 - 13x + 6

Warmup 8-28 Factor the following equations completely. Show work! (Check for GCF’s first) 6x2 + 30x - 216 4x2 - 12x + 5 3. 100 - 49x2 4. 75x2 - 27

Warmup 8-31 Factor the following equations completely. Show work! (Check for GCF’s first) 7x2 - 56x + 84 3x2 - 4x - 15 3. 20x2y – 35xy2 – 45x2y2 4. 121x2 - 25

Warmup 9-2 Factor the following equations completely. Show work!(Check for GCF’s first) 2x2 + 22x - 120 4x2 - 16x + 7 3. 20x2 – 45x 4. Solve the following factored equation. Show work! -2(x – 8)(3x + 4) = 0

Warmup 9-3 Factor the following equations completely. Show work! (Check for GCF’s first) 4x2 - 36x + 72 6x2 - 5x – 4 3. 9x2 + 45x 4. 25x2 - 64

Warmup 9-2 Factor the following equations completely. Show work! (Check for GCF’s first) 4x2 - 36x + 72 6x2 - 5x – 4 3. 9x2 + 45x 4. Solve the following factored equation. Show work! 3x(x + 5)(2x - 3) = 0

Warmup 9-4 Solve the following equations by factoring. Show work! (Check for GCF’s first) 2x2 + 6x – 56 = 0 2x2 - 21x + 27 = 0 3. 15x2 - 9x = 0 4. 4x2 - 49 = 0

Warmup 9-8 Solve the following equations by factoring. Show work! (Check for GCF’s first) 3x2 - 4x - 15 = 0 2. 12x2 + 20x = 0 3. 100x2 - 81 = 0

Warmup 9-9 Solve the following equations by factoring. Show work! 1. 2x2 - 22x + 48 = 0 2. 4x2 + 3x - 10 = 0 3. Solve by using the quadratic formula: 5x2 - 8x + 2 = 0

Warmup 9-9 Solve the following equations by factoring. Show work! 4x2 + 3x - 10 = 0 Solve by using the quadratic formula: 5x2 - 8x + 2 = 0 Solve by taking the square root: 3x2 – 25 = 56

Examples – Quadratic Formula Solve each quadratic equation below using the quadratic formula. Show work! 1. x2 + 5x - 24 = 0 2. 6x2 -17x + 12 = 0 3x2 - 8x - 2 = 0 4. 5x2 + 6x - 3 = 0 5. 7x2 - 11x + 2 = 0 6. 2x2 + 9x - 3 = 0 7. x2 + 14x + 49 = 0 8. 25x2 – 60x + 36 = 0

Geometry Quadratic Formula Practice Use the quadratic formula to solve the following quadratic equations. Show work! x2 + 9x – 36 = 0 2. x2 – 7x – 44 = 0 x2 – 11x – 102 = 0 4. 3x2 – 10x + 8 = 0 5x2 + 2x – 16 = 0 6. 27x2 – 15x + 2 = 0 5x2 – 6x – 1 = 0 8. x2 + 4x – 19 = 0 6x2 – 12x – 1 = 0 10. 3x2 – 6x – 4 = 0 3x2 + 10x - 2 = 0 12. 2x2 – 8x - 7 = 0

Geometry Quadratic Formula Practice 13. x2 – 10x + 25 = 0 14. x2 + 22x + 121 = 0 15. 9x2 – 24x + 16 = 0 16. 81x2 – 90x + 25 = 0 3x2 – 7x + 2 = 0 18. 2x2 – 11x + 7 = 0 4x2 -13x + 8 = 0 20. x2 – 6x + 25 = 0 4x2 - 8x + 13 = 0 22. x2 - 7x + 19 = 0 23. 5x2 -10x + 14 =0 24. 3x2 – 4x + 8 = 0

Ticket In the Door 9-9 Quadratic Formula Solve each quadratic equation below using the quadratic formula. Show work! 1. x2 – 8x - 20 = 0 2. 2x2 + 6x – 5 = 0 3. 4x2 – 7x + 2 = 0 4. 9x2 – 48x + 64

Analytic Geometry Factoring Practice Factor completely . Show work! 5x3 – 25x 2. x2 – 8x – 65 4x2 – 12x + 36 4. 3x2 - 42x + 144 2x2 – 36x – 126 6. 8x2 + 6x - 5 7. 12x2 – 2x – 14 8. 38x2y – 27xy2 2x2 – 11x + 12 10. 5x2 + 80x – 180 42x3 – 35x2 12. x2 - 20x + 100 13. x2 - 15x + 54 14. 15x – 60x2 15. 4x2 + 28x + 40 16. 9x2 – 30x + 24

18x2y – 9xy + 54x3y2 18. x2 - 28x + 75 19. 6x2 + 42x - 180 20. 8x4 – 12x3 – 20x2 + 48x

Ticket in the Door 8-27(Factoring) Factor the following equations completely. Show work! x2 - 4x - 45 2. 3x2 - 14x + 8 48x2y - 84xy2 4. 25x2 – 90x + 45 5. 4x2 – 16x - 128

Ticket Out the Door 9-1(Difference of Squares) Factor the following equations completely. Show work! 49x2 - 4 2. 64x2 - 121 81 - 25x2 4. 9x2 – 16 5. 50x2 - 98

Examples - Completing the Square A = 1 Examples Ex. x2 – 10x + 21 = 0 Ex. y2 – 14y – 51 = 0 Ex. x2 + 16x – 24 = 0 Ex. y2 + 12y - 27 = 0 Ex. x2 – 8x + 11 = 0 Ex. y2 + 18y + 68 = 0

Standard to Vertex Form Conversion Practice For the following quadratic equations, convert each one into vertex form. Then, identify the vertex and Axis of Symmetry. Show work! y = x2 – 8x + 19 y = -x2 - 14x - 35 3. y = -2x2 + 12x + 21 4. y = 3x2 + 30x - 56 5. y = -4x2 + 16x - 9 6. y = -x2 - 20x - 37 7. y = 5x2 -+ 40x + 63 y = 4x2 + 24x + 36 9. y = 2xw – 4x + 19 10. y = -3x2 – 12x 11. y = -6x2 + 24x - 11 y = 8x2 - 48x

Examples - Converting from standard to vertex form For the following quadratic equations, convert each one into vertex form. Then, identify the vertex and Axis of Symmetry. Show work! y = x2 – 12x + 28 y = x2 + 4x - 3 3. y = -x2 + 10x - 22 4. y = -x2 - 8x - 11 5. y = 2x2 + 4x + 1 6. y = -3x2 + 12x - 19 7. y = 4x2 + 24x + 41

Ticket In the Door 9-10 Convert from standard to vertex form For the following quadratic equations, convert each one into vertex form. Then, identify the vertex and Axis of Symmetry. Show work! y = x2 – 10x + 17 y = -x2 + 18x - 75 3, y = 4x2 + 8x + 9 4. y = -5x2 - 30x - 32

Warmup 9-11 Solve the following equations by factoring. Show work! x2 + 16x - 80 = 0 Solve by using the quadratic formula: 4x2 - 5x - 2 = 0 Solve by taking the square root: 6x2 + 17 = 167

Warmup 9-10 Solve the following equations by factoring. Show work! 3x2 + 15x - 72 = 0 5x2 - 14x + 8 = 0 3. Solve by using the quadratic formula: 6x2 - 7x - 3 = 0 4. Solve by using the quadratic formula: 3x2 - 10x + 5 = 0

Examples- Rate of Change From an Equation Find the rate of change of each quadratic equation below for the given interval(x – values) Show work! x2 - 4x – 6 from x = 2 to x = 4 x2 + 8x + 11 from x = -2 to x = -5 x2 - 12x + 43 from x = 3 to x = 7 2x2 - 16x + 19 from x = 2 to x = 5 3x2 + 12x + 5 from x = -2 to x = 0 6. 4x2 - 24x + 21 from x = 2 to x = 6

Rate of change from an equation practice Find the rate of change of each quadratic equation below for the given interval(x – values) Show work! y = x2 – 8x + 21 from x = 2 to x = 4 y = -x2 - 14x - 38 from x = -5 to x = -8 3. y = -2x2 + 12x – 22 from x = 1 to x = 6 4. y = 3x2 + 30x + 65 from x = -5 to x = -2 5. y = -4x2 + 16x - 9 from x = 0 to x = 3 6. y = 5x2 - 40x + 71 from x = 4 to x = 6 7. y = 4x2 + 24x + 36 from x = -6 to x = -3 8. y = 2x2 – 4x + 17 from x = -1 to x = 3 y = -3x2 – 12x from x = -2 to x = 2 10. y = 8x2 - 48x from x = -5 to x = -2

Ticket out the Door 9-15 Rate of change from an equation Find the rate of change of each quadratic equation below for the given interval (x – values) Show work! y = x2 – 10x + 19 from x = 4 to x = 7 y = -2x2 - 28x – 94 from x = -7 to x = -4 3, y = 4x2 - 8x - 7 from x = 0 to x = 3

Geometry Graphing Quadratics in Standard Form with Tables Examples Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 1. y = x2 – 4x + 9 : Vertex Form: _____________ Vertex: ________ A. O S.: ________ 2. y = -x2 – 12x - 39 Vertex Form: ______________ Vertex: __________ y = 2x2 + 12x + 11 X Y X Y X Y

Geometry Graphing Quadratics in Standard Form with Tables Examples Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 4. y = -2x2 + 16x - 23 : Vertex Form: _____________ Vertex: ________ A. O S.: ________ 5. y = 3x2 + 30x + 69 Vertex Form: ______________ Vertex: __________ 6. y = -4x2 + 56x - 188 Vertex Form: ______________ X Y X Y X Y

Geometry Graphing Quadratics in Standard Form with Tables Practice Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 1. y = -x2 – 14x - 40 Vertex Form: _____________ Vertex: ________ A. O S.: ________ y = 2x2 – 12x + 13 Vertex Form: ______________ Vertex: __________ y = x2 - 16x + 54 X Y X Y X Y

Geometry Graphing Quadratics in Standard Form with Tables Practice Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 4. y = -2x2 – 20x - 49 : Vertex Form: _____________ Vertex: ________ A. O S.: ________ 5. y = 3x2 – 12x + 5 Vertex Form: ______________ Vertex: __________ 6. y = -3x2 - 6x + 5 X Y X Y X Y

Geometry Graphing Quadratics in Standard Form with Tables Practice Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 7. y = -x2 + 8x - 13 Vertex Form: _____________ Vertex: ________ A. O S.: ________ 8. y = 4x2 + 24x + 30 Vertex Form: ______________ Vertex: __________ 9. y = -4x2 + 40x - 90 X Y X Y X Y

Geometry Graphing Quadratics in Vertex Form with Tables(Examples) Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 1. y = (x - 4)2 + 3 Vertex: ________ A. O S.: ________ 2. y = -(x + 3)2 - 2 y = (x + 5)2 - 4 X Y X Y X Y

Geometry Graphing Quadratics in Vertex Form with Tables(Examples) Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 4. y = 2(x + 1)2 - 6 Vertex: ________ A. O S.: ________ 5. y = -2(x - 5)2 + 3 6. y = -3(x + 7)2 + 2 X Y X Y X Y

Geometry Graphing Quadratics in Vertex Form with Tables Practice Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 1. y = (x + 2)2 - 7 Vertex: ________ A. O S.: ________ 2. y = -(x - 5)2 - 4 y = (x + 3)2 + 6 X Y X Y X Y

Geometry Graphing Quadratics in Vertex Form with Tables Practice Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 4. y = 2(x - 4)2 - 9 Vertex: ________ A. O S.: ________ 5. y = -2(x + 8)2 - 2 6. y = 3(x - 1)2 - 4 X Y X Y X Y

Geometry Graphing Quadratics in Vertex Form with Tables Practice Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 7. y = -3(x + 2)2 + 5 Vertex: ________ A. O S.: ________ 8. y = 4(x + 1)2 - 9 9. y = -4(x - 3)2 + 7 X Y X Y X Y

Ticket in the door 9-14 Graphing quadratics from standard form Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work! 1. y = x2 – 6x + 7 : Vertex Form: _____________ Vertex: ________ A. O S.: ________ 2. y = -2x2 + 28x - 93 Vertex Form: ______________ Vertex: __________ y = 3x2 + 30x + 71 X Y X Y X Y

Ticket out the Door 9-10(2) Graphing Quadratics in vertex form Identify the vertex and Axis of Then graph the quadratic equations by making a table of values. Show work! 1. y = (x + 6)2 - 5 Vertex: ________ A. O S.: ________ 2. y = -2(x - 3)2 + 4 3. y = 3(x + 5)2 - 9 X Y X Y X Y

Warmup 9-14 X Y 1.Solve by using the quadratic formula: 3x2 - 10x + 5 = 0 2. Solve by taking the square root: 8x2 - 47 = 121 3. Graph the following quadratic equation using the table provided. x2 + 8x + 13 Vertex: __________ A.O.S. : __________ Extrema: ________ X Y

Warmup 9-15 X Y 1.Solve by using the quadratic formula: 4x2 - 13x - 12 = 0 2. Solve by taking the square root: 5x2 + 53 = 428 3. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. -x2 + 6x - 14 Vertex: __________ Up or down: _______ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Extrema: ________ y-int: _________ X Y

Warmup 9-16 1. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. -x2 + 6x - 14 Vertex __________ A. O. S. : ________ Extrema: _______ 2. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. 2x2 + 16x + 25 Vertex: __________ Extrema: _________ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Rate of Change -6 < x < -3: _________ X Y X Y

Warmup 9-16 X Y 1.Solve by using the quadratic formula: 3x2 + 11x + 4 = 0 2. Solve by taking the square root: 6x2 - 76 = 20 3. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. 2x2 + 16x + 25 Vertex: __________ Extrema: _________ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Rate of Change -6 < x < -3: _________ X Y

Warmup 9-17 1. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -x2 - 10x - 29 Vertex: __________ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Extrema: ________ 2. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = 3x2 - 24x + 42 X Y X Y

Warmup 9-18 1. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -3x2 + 12x - 8 Vertex: __________ Up or down: _______ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Extrema: ________ y-int: _________ Find the rate of change for the graph above for: 1 < x < 4. 3. In the equation, h(t) = -9t2 + 90t + 75, What does the t represent? b. What does the h(t) represent? X Y

Warmup 9-18 1. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -3x2 + 12x - 8 Vertex: __________ Up or down: _______ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Extrema: ________ y-int: _________ If we were given the graph for the equation, h(t) = -4t2 + 40t. 2. Where on the graph of this equation would we look to find the time when the maximum height occurred? Where on the graph of this equation would we look to find the maximum height of the object? 4. Where on the graph of this equation would we look to find the initial height of the object? X Y

Warmup 9-28 1. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -3x2 + 12x - 8 Vertex: __________ Extrema: _______ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Rate of Change 0<x<3 : _________ For the following questions, use the equation, h(t) = -6t2 + 36t + 76. 2. Find the height of the object at 5 seconds, or h(5). 3. What is the initial height of the object? 4. At what time did the object reach its maximum height? 5. What was the maximum height of the object? X Y

Warmup 9-30 1. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -x2 - 14x -43 Vertex: __________ Extrema: _______ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Rate of Change -7<x<-5 : _________ For the following questions, use the equation, h(t) = -3t2 + 24t. 2. Find the height of the object at 7 seconds, or h(7). 3. What is the initial height of the object? 4. At what time did the object reach its maximum height? What was the maximum height of the object? For what time interval was the object going down? X Y

Warmup 10-1 For the following questions, use the equation, h(t) = -5t2 + 30t + 35. 1. Find the height of the object at 5 seconds, or h(5). 2. What is the initial height of the object? 3. At what time did the object reach its maximum height? 4. What was the maximum height of the object? For what time interval was the object going up? Complete the square for the following equation: x2 – 14x + 33 = 0 7. Complete the square for the following equation: y2 + 20y - 44 = 0

Warmup 10-2 For 1-2, write an equation of a circle in standard form for the given information. 1. Center = (7, 0) and r = 43 2. Center = (8, -3) and r = 13 For the following circle equations, identify the center and radius. 3. (x - 7)2 + (y + 3)2 = 81 4. Solve by completing the square. Show work! x2 + 16x - 26 = 0

Geometry Standard Form Analysis 1. Vertex: __________ Up or down: _______ A. O. S. : __________ Domain: ___________ Range: ____________ y-int: _________ 2. Vertex: __________ Up or down: _______ 3. Vertex: __________ Up or down: _______ 4. Vertex: __________ Up or down: _______ 5. Vertex: __________ Up or down: _______ Range: ____________ 7. Vertex: _______ y-int: _________ A.O.S. : _______ Domain: ________ 6. Vertex: __________ Up or down: _______ Range: ________ A. O. S. : __________ Y-int: ________ Domain: ___________ Up or Down: _______

8. Vertex: __________ Up or down: _______ A. O. S. : __________ Domain: ___________ Range: ____________ y-int: _________ 9. Vertex: __________ Up or down: _______ 10. Vertex: __________ Up or down: _______ 11. Vertex: __________ Up or down: _______ 12. Vertex: __________ Up or down: _______ Range: ____________ 14. Vertex: _______ y-int: _________ A.O.S. : _______ Domain: ________ 13. Vertex: __________ Up or down: _______ Range: ________ A. O. S. : __________ Y-int: ________ Domain: ___________ Up or Down: _______

Notes - Quadratic Applications Basic Equation Terms: h(t) = -at2 + bt + c t = time in seconds h(t) = height of object at t seconds. Questions about graphs of quadratic applications. What part of a quadratic graph represents: The height of the object at a given time? The initial height of the object when it is thrown/launched? 3. The time when the object reaches its maximum height? 4. The maximum height of the object? The time when the object hits the ground? The total time the object is in the air? Questions about dealing with a quadratic application equation. How do we find the height of the object at a given time? 2. How do we find the time the object reaches its maximum height? 3. How do we find the maximum height of the object? 4. Where in the equation can we find the initial height of the object?

Ticket out the door 9-16 For the following questions, use the graph from the equation, h(t) = -3t2 + 36t. (on the back of one of the graphs used in the notes) What is the height of the object at 9 seconds or h(9)? What is the initial height of the object? At what time did the object reach its maximum height? What was the maximum height of the object? When did the object land on the ground? How long was the object in the air? For the following questions, use the equation, h(t) = -4t2 +48t + 56 7. What is the height of the object at 2 seconds or h(2)? 8. What is the initial height of the object? 9. At what time did the object reach its maximum height? 10. What was the maximum height of the object?

Ticket out the door 9-17 For the following questions, use the graph from the equation, h(t) = -3t2 + 36t. (on the back of one of the graphs used in the notes) What is the height of the object at 9 seconds or h(9)? What is the initial height of the object? At what time did the object reach its maximum height? 4. What was the maximum height of the object? 5. When did the object land on the ground? How long was the object in the air?

Ticket out the door 9-28 For the following questions, use the graph from the equation, h(t) = -5t2 + 30t + 55. (on the back of one of the graphs used in the notes) What is the height of the object at 7 seconds or h(7)? What is the initial height of the object? At what time did the object reach its maximum height? What was the maximum height of the object? For the following questions, use the equation, h(t) = -2t2 +32t 5. What is the height of the object at 3 seconds or h(3)? 6. What is the initial height of the object? 7. At what time did the object reach its maximum height? 8. What was the maximum height of the object?

Warmup 9-29 For the following questions, use the graph from the equation, h(t) = -4t2 + 48t. (on the back of one of the graphs used in the notes) What is the height of the object at 2 seconds or h(2)? What is the initial height of the object? At what time did the object reach its maximum height? What was the maximum height of the object? For the following questions, use the equation, h(t) = -3t2 + 54t + 27 5. What is the height of the object at 6 seconds or h(6)? 6. What is the initial height of the object? 7. At what time did the object reach its maximum height? 8. What was the maximum height of the object?

Mini Quiz Quadratic Applications For the following questions, use the graph from the equation, h(t) = -5t2 + 60t + 15. What is the height of the object at 4 seconds or h(4)? What is the initial height of the object? At what time did the object reach its maximum height? 4. What was the maximum height of the object? 5. For what time interval was the object going up? For the following questions, use the graph of the equation, h(t) = -3t2 + 24t 6. What is the height of the object at 7 seconds or h(7)? 7. What is the initial height of the object? 8. At what time did the object reach its maximum height? 9. What was the maximum height of the object? 10. When did the object hit the ground? 11. For what time interval was the object going down?

Mini Quiz Quadratic Applications For the following questions, use the equation, h(t) = -4t2 + 64t. 12. What is the height of the object at 5 seconds or h(5)? 13. What is the initial height of the object? 14. At what time did the object reach its maximum height? 15. What was the maximum height of the object? 16. For what time interval was the object going up? For the following questions, use the graph of the equation, h(t) = -7t2 + 42t + 57 17. What is the height of the object at 4 seconds or h(4)? 18. What is the initial height of the object? 19. At what time did the object reach its maximum height? 20. What was the maximum height of the object? 21. For what time interval was the object going up?

Ticket out the door 9-18 For the following questions, use the equation, h(t) = -4t2 +48t + 56 1. What is the height of the object at 2 seconds or h(2)? 2. What is the initial height of the object? 3. At what time did the object reach its maximum height? 4. What was the maximum height of the object? 5. In what time interval would the object be going up?

Quadratic Application Practice For the following questions, use the graph from the equation, h(t) = -2t2 + 20t. What is the height of the object at 3 seconds or h(3)? What is the initial height of the object? At what time did the object reach its maximum height? What was the maximum height of the object? When did the object land on the ground? How long was the object in the air? For the following questions, use the graph from the equation, h(t) = -5t2 + 40t + 100. 7. What is the height of the object at 9 seconds or h(9)? 8. What is the initial height of the object? 9. At what time did the object reach its maximum height? 10. What was the maximum height of the object? 11. When did the object land on the ground? 12. How long was the object in the air?

Quadratic Application Practice For the following questions, use the equation, h(t) = -3t2 + 54t 13. What is the height of the object at 7 seconds or h(7)? 14. What is the initial height of the object? 15. At what time did the object reach its maximum height? 16. What was the maximum height of the object? For the following questions, use the equation, h(t) = -5t2 + 30t + 75 17. What is the height of the object at 4 seconds or h(4)? 18. What is the initial height of the object? 19. At what time did the object reach its maximum height? 20. What was the maximum height of the object?

Quadratic Application Review For the following questions, use the graph from the equation, h(t) = -6t2 + 60t. What is the height of the object at 4 seconds or h(4)? What is the initial height of the object? At what time did the object reach its maximum height? What was the maximum height of the object? When did the object land on the ground? How long was the object in the air? For the following questions, use the graph from the equation, h(t) = -8t2 + 64t + 32. 7. What is the height of the object at 6 seconds or h(6)? 8. What is the initial height of the object? 9. At what time did the object reach its maximum height? 10. What was the maximum height of the object? 11. When did the object land on the ground?(Approximately) 12. How long was the object in the air? Approximately)

Quadratic Application Review For the following questions, use the equation, h(t) = -4t2 + 48t 13. What is the height of the object at 4 seconds or h(4)? 14. What is the initial height of the object? 15. At what time did the object reach its maximum height? 16. What was the maximum height of the object? For the following questions, use the equation, h(t) = -7t2 + 56t + 84 17. What is the height of the object at 6 seconds or h(6)? 18. What is the initial height of the object? 19. At what time did the object reach its maximum height? 20. What was the maximum height of the object?

Examples – Completing the Square A = 1 Examples Ex. x2 – 10x + 18 = 0 Ex. x2 + 16x – 24 = 0 Ex. y2 – 8y – 12 = 0 Ex. y2 + 2y + 9 = 0

Ticket out the Door 9-30 Complete the square in each problem below. Show work! 1. x2 – 18x + 45 = 0 2. y2 + 8x – 56 = 0 3. y2 – 6y + 18 = 0 4. x2 + 4x - 9 = 0

Completing the Square Practice Complete the square in each problem below. Show work! 1. x2 + 4x - 12 = 0 2. x2 – 10x - 56 = 0 3. x2 - 22x + 84 = 0 4. y2 + 16x – 60 = 0 5. y2 – 28y + 150 = 0 6. y2 - 24y – 96 = 0 x2 + 12x - 108 = 0 8. x2 – 12x + 15 = 0 x2 + 6x - 13 = 0 10. y2 – 2y + 11 = 0

Examples – Circles in Standard Form Part 1 Standard Form for a Circle Equation: (x - h)2 + (y – k)2 = r2 center of circle is (h, k) (opposite of each number in parenthesis) r = radius of circle (must take square root of r2 to get r ) Writing the equation of a circle in standard form given the center and radius. Ex. Center = (2.-3) , radius = 6 Ex. Center = (-4, 0), radius = 3 Ex. Center = (7, 8), radius = 10 (remember, squaring a square root cancels it out) Ex. Center = (5, -1), radius = 23 Given the equation in standard form, identify the center, radius and diameter. Ex. x2 + y2 = 144 Ex. x2 + (y – 2)2 = 36 Ex. (x + 4)2 + y2 = 81 Ex. (x – 6)2 + (y + 3)2 = 25 Ex. (x + 1)2 + (y – 9)2 = 121

Examples – Circles in Standard Form Part 2 Standard Form for a Circle Equation: (x - h)2 + (y – k)2 = r2 center of circle is (h, k) (opposite of each number in parenthesis) Use completing the square to write a circle equation in standard form. Then identify the center, radius, and diameter of the circle: Ex. x2 -12x + y2 -13 = 0 Ex . x2 + y2 + 8y – 105 = 0 Ex. x2 + 10x + y2 – 39 = 0 Ex. x2 + y2 – 6y - 72 = 0

Ticket in the door 10-2 Write the equation of a circle in standard form for the given information. Show work! 1. Center = (-2-5), r = 7 2 Center = (0, -8), r = 35 For the following circle equations written in standard form, identify the center, and radius. 3. (x + 7)2 + y2 = 25 4. (x – 3)2 + (y + 4)2 = 196 Complete the square in each problem below. Show work! 5. x2 – 18x + 45 = 0 6. y2 + 8x – 56 = 0

Ticket out the Door 10-1 For #1- 2, use completing the square to write the circle equation in standard form. THEN, LIST the Center, and Radius. Show work! x2 + y2 – 18y – 88 = 0 2. x2 – 12x + y2 – 45 = 0

Warmup 10-6 For #1 below, write an equation of a circle in standard form for the given information. 1. Center = (7, -12) and r = 36 Complete the square in the problem below. Show work! y2 - 14y - 5 = 0 For the following circle equations, identify the center and radius. (Complete the square in 4 and 5 first.) 3. (x – 9)2 + y2 = 225 x2 + 16x - 132 + y2 = 0 (x + 3)2 + y2 - 6x - 112 = 0

Geometry Mini Quiz Completing the Square and Circles in standard form For 1-2, write an equation of a circle in standard form for the given information. 1. Center = (-5, 4) and r = 52 2. Center = (0, -6) and r = 8 Complete the square in the problems below. Show work! 3. x2 + 22x + 41 = 0 4. y2 – 14y - 95 = 0 For the following circle equations, identify the center and radius. (Complete the square if needed first) 5. x2 + (y + 7)2 = 169 6. (x – 5)2 + (y + 9)2 = 256 7. (x + 6)2 + y2 - 20y - 44 = 0 8. x2 + 20x + 19 + y2 = 0

Warmup 10-8 For 1-3, write an equation of a circle in standard form for the given information. 1. Center = (4, -5) and r = 16 For the following circle equations, identify the center and radius. 2. (x – 8)2 + y2 - 10x – 171 = 0 Find the distance and midpoint for the following pair of points. Show work! (-5, 2) and (3, -4) Find the slope of the following two points. Show work! (-3, 7)(11, -1)

Warmup 10-7 For 1-3, write an equation of a circle in standard form for the given information. 1. Center = (0, -9) and r = 21 2. Center = (-5, 7) and r = 8 For the following circle equations, identify the center and radius. 3. (x + 3)2 + (y – 11)2 = 49 4. x2 + 14x - 32 + (y + 6)2 = 0 5. x2 + y2 – 12y + 27 = 0

Warmup 10-9 1. Find the distance and midpoint for the following pair of points. Show work! (-6, -5) and (-10, 2) 2. Find the slope of the following two points. Show work! (-3, 5)(13, -5) Use the slope, distance, or midpoint formula with the following set of 4 points to determine whether they represent a rhombus, rectangle, or square.(must show they make a parallelogram first!) A(2.-1) B(4, 2) C(7, -4) D(9, -1)

Warmup 10-12 1. Find the distance and midpoint for the following pair of points. Show work! (4, 1) and (-11, 9) 2. Find the slope of the following two points. Show work! (-8, 5)(4, -5) Use the slope, distance, or midpoint formula with the following set of 4 points to determine whether they represent a rhombus, rectangle, or square.(must show they make a parallelogram first!) A(-3.5) B(1, -1) C(-2, -3) D(-6, 3)

Warmup 10-15 1. Find the distance and midpoint for the following pair of points. Show work! (-4, -7) and (2, -10) 2. Find the slope of the following two points. Show work! (5, 9)(-4, 30) Find the area and circumference of a circle with a diameter = 30cm. Find the volume of a cylinder with a diameter = 12m and a height of 7m. Find the volume of a cone with a radius = 15mm and a height of 9mm.

Warmup 10-15 For #1-4, use the volume of a cone or cylinder formula to help solve each problem. Show work! How many cubic feet of water would fit in a cylindrical pool that has a diameter of 24ft and a height of 6ft? How many cubic inches of ice cream would fit in a cone that has a radius of 4 inches and a height of 10 inches? A person has two cans of soup. The first can has a radius of 8cm, and a height of 14cm. The second can has a diameter of 20cm, and a height of 9cm. Which can has more soup in it? A company currently produces a cone shaped paper cup with a diameter of 4 inches and a height of 5 inches. They are looking into making a new design which will have a radius of 3 inches and a height of 6 inches. How much more water will fit into the newer version?

Warmup 10-16 In a subdivision, all of the lots are arranged as quadrilaterals. Lot 1 has dimensions of 60ft, 90ft, 75ft, and 105ft. Lot 2 has dimensions of 96ft, 168ft, 120ft, and 144ft. Do these two lots for similar polygons? Show why or why not. In a subdivision, all of the lots are arranged as quadrilaterals. Lots 3 and 4 are similarly shaped. Lot 3 has dimensions of 96ft, 160ft, 196ft, and 128ft. Lot 4 has dimensions of 108ft, 81ft, 162ft, and 135ft. What would the scale factor be from Lot 4 to Lot 3? In a subdivision, 2 neighbors want to have rectangular in-ground pools put in. Neighbor 1 plans to have their pool be 42ft long and 18ft wide. Neighbor 2 knows that their pool will need to be 35ft long. How wide should neighbor 2’s pool be to make the two pools similarly shaped? Instant oats come in packages that are cylinder shaped. A store sells two sizes of these oats. The smaller package has a diameter of 8in and a height of 15in. The larger package has a radius of 6in and a height of 20in. How many more cubic inches of oats are in the larger cylinder?

Warmup 10-28 If a cedar chest has a base that is 54 inches by 27 inches, and is 20 inches tall, how many cubic inches of storage space does it have? A roof is 24 feet across the base, and is 14 feet high. If the roof is 45 feet long, what is the storage space of the attic inside the roof? A box of Oxy-Clean is 25cm by 25cm by 42cm. How many cubic centimeters of detergent can the box hold? Two neighbors are having in-ground pools installed at their homes. Neighbor 1 plans to have a pool that is 45ft long by 20ft wide, by 10ft deep. Neighbor 2 wants their pool to be 42ft long by 24ft wide, by 9ft deep. Which neighbor’s pool will hold more water? The company who makes tootsie rolls is considering changing their packaging from a cylinder to a triangular prism. Their current packaging has a diameter of 4 inches and a height of 16 inches. The new design has a base that is 6 inches, and a height of 5 inches. If the height of the prism is still 16 inches, how many more cubic inches of tootsie rolls will fit in the new package design? (must get a decimal from multiplying by pi in the cylinder volume)

Mini Quiz Midpoint, Distance, Slope, Area, Circumference and Volume Formulas 1. Find the distance and midpoint for the following pair of points. Show work! (-3, 7 ) and (-10, -17) 2. Find the slope of the following two points. Show work! (-8, 5)(-24, -9) Use the slope, distance, or midpoint formula with the following set of 4 points to determine whether they represent a rhombus, rectangle, or square.(must show they make a parallelogram first!) E(4, 7) F(7, 3) G(4, -1) H(1, 3)

Mini Quiz Midpoint, Distance, Slope, Area, Circumference and Volume Formulas Find the area of a circle with a diameter = 26in. Show work! Find the circumference of a circle with a radius = 17ft. Show work! 6. Find the volume of a cylinder with a radius = 18m, and a height = 12m. Show work! Find the volume of a cone with a diameter = 42cm, and a height = 15cm. Show work!

Special Quadrilateral Coordinate Geometry Practice Use the slope, distance, or midpoint formula with the following set of 4 points to determine whether they represent a rhombus, rectangle, or square.(must show they make a parallelogram first!) A(-5, 4) B(-2, 6) C(2, 0) D(-1, -2) 2. E(-8,5) F(1. -2) G(-5,-6) H(4, -13) 3. I(1, 4) J(5,5) K(3, -4) L(7, -3) M(-6, 2) N(-3, 0) P(-1, 3) Q(-4, 5) 5. R(-5, -1) S(-4, 6) T(0, 4) U(1, 11) 6. V(4,4) W(0, -2) X(-6, 2) Y(-2, 8) Z(-2, 5) A(2, 8) B(4.-3) C(8, 0) 8. D(0, 5) E(-2, 14) F(4, 7) G(6, -2)

Ticket in the Door 10-9 Special Quadrilaterals Coordinate Geometry Use the slope, distance, or midpoint formula with the following set of 4 points to determine whether they represent a rhombus, rectangle, or square.(must show they make a parallelogram first!) A(-2, 3) B(2, 6) C(7, 6) D(3, 3) 2. E(1, 1) F(5. 3) G(4, 5) H(0, 3)

Warmup 10-8 1. Use the slope, distance, or midpoint formula with the following set of 4 points to determine whether they represent a rhombus, rectangle, or square.(must show they make a parallelogram first!) E(-6.-2) F(-4, -5) G(-6, -8) H(-8, -5) Find the area of circle with a radius = 14(leave answer in terms of pi.) Find the circumference of a circle with a radius = 17.(leave answer in terms of pi.)

Circles in Standard Form Practice Write the equation of a circle in standard form for the given information. 1. Center = (0,0) , r = 12 2. Center = (0, 0), r = 2 7 3 . Center = (2, -5), r = 15 4. Center = (-4, 3), r = 62 Center = (0, -8), r = 11 6. Center = (9, 0), r = 45 Center = (-12, -5), r = 18 8. Center = (7, 10), r = 1.5 For #9-14, use completing the square to write the circle equation in standard form. THEN, LIST the Center, Radius, and Diameter. Show work! 9. x2 - 4x + y2 = 21 10. x2 + y2 + 16y = 36 4x2 + 4y2 – 40y = 224 12. 9x2 + 54x + 9y2 = 63 13. 7x2 – 14x + 7y2 + 56x = 133 14. 6x2 + 48x + 6y2 – 24x = 606

Circles in Standard Form Practice(Part 2) In the following problems, use completing the square to write the circle equation in standard form. THEN, LIST the Center, Radius, and Diameter. Show work! 1. x2 - 4x + y2 – 21 = 0 2. x2 + y2 + 16y – 36 = 0 3. x2 + y2 – 10y - 56 = 0 4. x2 + 6x + y2 - 7 = 0 5. x2 - 26x + y2 + 105 = 0 6. x2 + y2 + 28y + 96 = 0 x2 – 2x - 35 + (y + 4)2 = 0 8. (x - 6)2 + y2 – 16y - 161 = 0 9. (x + 5)2 + y2 – 14y + 13 = 0 10. x2 - 20x – 96 + (y – 9)2 = 0 11. (x – 12)2 + y2 + 4y - 5 = 0 12. x2 - 22x + 117 + (y + 3)2 = 0

Circles in Standard Form Practice(1) Write the equation of a circle in standard form for the given information. 1. Center = (0,0) , r = 19 2. Center = (0, 0), r = 210 3 . Center = (0, -7), r = 24 4. Center = (5, 0), r = 37 Center = (-1, -4), r = 21 6. Center = (3, -6), r = 47 Center = (11, 3), r = 27 8. Center = (-9, 2), r = 3.5 Center = (10, -12), d = 14 10. Center = (3, 5), d = 32 Center = (0, -6), d = 30 12. Center = (-13, 0) , d = 8 For #13-18, identify the center, radius, and diameter of each circle. 13. (x – 8)2 + y2 = 81 14. x2 + y2 = 289 15. (x - 2)2 + (y + 4)2 = 225 16. (x + 1)2 + (y + 7)2 = 484 17. (x - 5)2 + (y - 12)2 = 4 18. (x + 3)2 + (y – 9)2 = 42

Circles in Standard Form Practice Write the equation of a circle in standard form for the given information. 1. Center = (0,0) , r = 12 2. Center = (0, 0), r = 2 7 3 . Center = (2, -5), r = 15 4. Center = (-4, 3), r = 62 Center = (0, -8), r = 11 6. Center = (9, 0), r = 45 Center = (-12, -5), r = 18 8. Center = (7, 10), r = 1.5 Center = (-8, 0), d = 14. 10. Center = (6, -7), d = 22 Center = (0, 12), d = 34 12. Center = (-9, -2) , d = 18 For #13-18, identify the center, radius, and diameter of each circle. 13. x2 + (y + 4)2 = 49 14. (x – 5)2 + y2 = 100 15. (x + 7)2 + (y – 1) 2 = 196 16. (x – 9)2 + (y + 6)2 = 121 17. (x + 4)2 + (y + 10)2 = 1 18. (x – 2)2 + (y – 8)2 = 10

Parallel Lines cut by a Transversal Practice 3 5 For the following problems, name 1 pair of angles in the picture at the right that fits each type listed below. 1. Alternate exterior 2. Same Side Interior 3. Vertical Angles 4. Alternate Interior 5. Corresponding 6. Supplementary In the figure, Line L is parallel to Line M. For #7-14, tell what type of angles each pair listed is AND tell whether the angles are congruent(=) or supplementary(add to = 180). 7. <2, <5 8. <7, <3 9. <3,<6 10. <2, <7 11. <1, <4 12. <6, <8 13. <4, <7 14. <7, <8 For #15-20, use the figure at the right. Line L is parallel to Line M. If < 4 = 73, find the measure of each angle below and identify the type of angle each forms with <4. 15. <7 16. < 1 17. <5 18. <2 19. <8 20. Using the measure of <8 from #13, find the measure of <3 and give the type of angle. L 7 1 6 4 M 2 8 M t L 5 3 8 1 2 6 7 4 t 3 5 L 7 1 6 4 M 2 8

Parallel Lines cut by a Transversal Extra Practice 4 2 For the following problems, name 1 pair of angles in the picture at the right that fits each type listed below. 1. Alternate exterior 2. Same Side Interior 3. Vertical Angles 4. Alternate Interior 5. Corresponding 6. Supplementary In the figure, Line L is parallel to Line M. For #7-14, tell what type of angles each pair listed is AND tell whether the angles are congruent(=) or supplementary(add to = 180). 7. <2, <5 8. <6, <3 9. <3,<2 10. <2, <7 11. <8, <4 12. <7, <8 13. <3, <7 14. <2, <1 For #15-20, use the figure at the right. Line L is parallel to Line M. If < 4 = 58, find the measure of each angle below and identify the type of angle each forms with <4. 15. <7 16. < 1 17. <5 18. <2 19. <8 20. Using the measure of <7 from #13, find the measure of <3 and give the type of angle. L 7 5 6 3 M 1 8 M t L 4 3 5 6 1 7 2 8 t 3 5 L 1 8 6 4 M 2 7

Ticket out the Door 10-19 M t L 1 3 7 6 8 5 2 4 T 1 8 5 3 7 4 2 6 M L In the picture at the right, line L is parallel to line M. Name the type of angles given in each problem below. <5, <7 <2, < 8 <2, <3 <4, <6 <1, <7 <3, <5 In the picture at the right, Line L is parallel to Line M If <5 = 132, find the measure of the following angles. THEN, describe the type of angle each one forms with <5. 7. <7 8. <8 9. <4 10. <1 11. <2 t L 1 3 7 6 8 5 2 4 T 1 8 5 3 7 4 2 6 M L

Parallel Lines cut by a Transversal Practice(part 2) For the following problems, use the figure at the right. In the figure, Line L is parallel to Line M. Show work on all problems! 1. If <1 = 16x – 49, and <6 = 3x + 29, solve for x. 2. If <6 = 7x - 53, and <7 = 5x – 31, solve for x. 3. If <2 = 9x + 61, and <4 = 3x + 102, solve for x. 4. If <5 = 11x - 28, and <1 = 9x + 88, solve for x. 5. If <2 = 14x - 37 , and <5 = 5x - 1, solvefor x. 6. If <8 = 19x + 46, and <1 = 31x - 50, solve for x. 3 5 L 7 1 6 4 M 2 8 7. If <8 = 14x – 72, and <4 = 5x – 18, solve for x. 8. If <1 = 12x + 45, and <7 = 6x – 9, solve 9. If <5 = 19x - 33, and <7 = 5x + 65, solve 10 . If <6 = 8x + 73, and <4 = 21x – 44, solve 11. If <2 = 11x - 62, and <8 = 13x + 50, solve 12. If <8 = 17x - 23, and <6 = 25x – 119, solve 13. If <3 = 10x + 51, and <6 = 4x – 25, solve M t L 1 3 7 6 8 5 2 4

Examples – Parallel Lines cut by a Transversal (Part 2) 1. If line L is parallel to line M at the right, <3 = 12x – 42 and <1 = 7x + 23, solve for x. 2. If line L is parallel to line M at the right, <2 = 4x + 53, <4 = 11x - 8, solve for x. 3. If line L is parallel to line M at the right, < 5 = 21x + 73, and <7 = 5x + 121, solve for x. 4. If line L is parallel to line M, <1 = 15x - 59, and <8 = 19x - 103, solve for x. 5. If line L is parallel to line M, <6 = 11x + 82, and <2 = 18x - 16, solve for x. 6. If line L is parallel to line M, <4 = 8x - 63, and <7 = 12x - 57, solve for x. M 7 3 4 6 L 2 1 8 5

Ticket out the Door 10-21 T 8 1 7 2 5 3 6 4 M L 1. If line L is parallel to line M at the right, <8 = 11x – 31 and <4 = 7x + 25, solve for x. 2. If line L is parallel to line M at the right, <2 = 6x – 41, <6 = 4x -29, solve for x. 3. If line L is parallel to line M at the right, < 7 = 13x + 63, and <3 = 19x + 15, solve for x. 4. If line L is parallel to line M, <5 = 5x - 47, and <3 = 7x - 25, solve for x. T 8 7 1 5 2 3 6 4 M L

Warmup 10-21 In the picture at the right, line L is parallel to line M. Name the type of angles given in each problem below. THEN, tell whether each pair is = or add to = 180. <8, <4 <2, <8 <6, <7 <7, <2 <1, <8 6. <3, <4 In the picture at the right, Line L is parallel to Line M. If <3 = 141, find the measure of the following angles. Give a reason(type) for each answer. 7. <8 8. <7 9. <1 10. <4 What would <2 =?(compare it to <4 found in #10.) M t L 5 6 4 2 8 7 1 3 T 6 1 7 2 8 3 4 5 M L