1. Warmup 8-17(Geom) Add or subtract each set of polynomials.
Answers should be in standard form.
Show work!
1. (16x - 7x3 + 13) - (19x x)
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

2. Examples of Rational/Irrational #’s, Perfect Squares and Factors(Geom)
Identify whether each number below is rational
or irrational.
1. ½ √5 3. √16
-1/ π
√ √ √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:
Make a factor tree for the following numbers:

3. Rational vs. Irrational #’s, Perfect Squares and Factor Practice(Geom)
Identify whether each number below is rational
or irrational. Explain.
1. √ π 3. √81
4. -4/ √121
7. π/ √ √12
√25
Determine if the following numbers are perfect squares. Show why.
Make a factor tree for the following numbers:

4. Ticket out the Door 8-17(Geom)
Identify whether each number below is rational
or irrational. Explain.
√ π/ √
Determine if the following numbers are perfect squares. Show why.
Make a factor tree for the following numbers:

5. 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.
x-4y (5x2y-3)2
45xy2
4. Tell whether the following expressions are
examples of rational or irrational numbers.
11π b √49

6. 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 √37
Simplify: √(90x2y)
Add or subtract:
√ √48 + 2√75 - 4√125

7. 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)
x5y-3
28x-4y-1
3. Simplify: √(64x3y4)
4. Tell whether the following expressions are
examples of rational or irrational numbers.
5√144 b √37

8. 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)
x-7y-5
30x4y-9
3. (2x-4y8)5
4. Simplify: √(60x6y3)

9. 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.
π √25
Simplify each radical expression below. Show work!
3. √(28xy2) √(49x4y6.)
5. √(96xy3)
Combine like terms in the following radical expressions. Show work!
6. 2√96 - √90 - 3√ √ √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
x-3y (-5) -7 × (-5) 4
20x-8y-2

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

11. 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

12. 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
x2y - 9xy2 - 54x2y2

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

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

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

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

17. 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
x2 - 25

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

19. 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

20. 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

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

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

23. 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

24. 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

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

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

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

28. 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

29. Analytic Geometry Factoring Practice
Factor completely . Show work!
5x3 – 25x x2 – 8x – 65
4x2 – 12x x x + 144
2x2 – 36x – x2 + 6x - 5
x2 – 2x – x2y – 27xy2
2x2 – 11x x2 + 80x – 180
42x3 – 35x x x + 100
13. x x x – 60x2
x2 + 28x x2 – 30x + 24

30. 18x2y – 9xy + 54x3y x x + 75
x x x4 – 12x3 – 20x2 + 48x

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

32. Ticket Out the Door 9-1(Difference of Squares)
Factor the following equations completely. Show work!
49x x
x x2 – 16
5. 50x2 - 98

33. 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 = 0

34. 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 = -x x - 37
7. y = 5x x + 63
y = 4x2 + 24x + 36
9. y = 2xw – 4x + 19
y = -3x2 – 12x
y = -6x x - 11
y = 8x x

35. 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 y = 4x2 + 24x + 41

36. 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

37. 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:
6x = 167

38. 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

39. 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

40. 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 from x = 2 to x = 4
y = -x2 - 14x from x = -5 to x = -8
3. y = -2x2 + 12x – 22 from x = 1 to x = 6
4. y = 3x2 + 30x from x = -5 to x = -2
5. y = -4x2 + 16x from x = 0 to x = 3
6. y = 5x2 - 40x from x = 4 to x = 6
7. y = 4x2 + 24x from x = -6 to x = -3
8. y = 2x2 – 4x from x = -1 to x = 3
y = -3x2 – 12x from x = -2 to x = 2
10. y = 8x x from x = -5 to x = -2

41. 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 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

42. 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

43. 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 Vertex Form: ______________
Vertex: __________
6. y = -4x2 + 56x - 188
Vertex Form: ______________ X Y X Y X Y

44. 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

45. 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

46. 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

47. 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)
y = (x + 5)2 - 4 X Y X Y X Y

48. 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)
6. y = -3(x + 7)2 + 2 X Y X Y X Y

49. 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)
y = (x + 3)2 + 6 X Y X Y X Y

50. 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

51. 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

52. 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

53. 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

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

55. Warmup 9-15 X Y 1.Solve by using the quadratic formula:
4x2 - 13x - 12 = 0
2. Solve by taking the square root:
5x = 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

56. 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

57. Warmup 9-16 X Y 1.Solve by using the quadratic formula:
3x2 + 11x + 4 = 0
2. Solve by taking the square root:
6x = 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

58. 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

59. 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

60. 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

61. 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).
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

62. 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).
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

63. 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).
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

64. 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

65. 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: ____________ Vertex: _______
y-int: _________ A.O.S. : _______
Domain: ________
6. Vertex: __________ Up or down: _______ Range: ________
A. O. S. : __________ Y-int: ________
Domain: ___________ Up or Down: _______

66. 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: ____________ Vertex: _______
y-int: _________ A.O.S. : _______
Domain: ________
13. Vertex: __________ Up or down: _______ Range: ________
A. O. S. : __________ Y-int: ________
Domain: ___________ Up or Down: _______

67. 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?

68. 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?
At what time did the object reach its maximum height?
10. What was the maximum height of the object?

69. 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?
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?

70. 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?
At what time did the object reach its maximum height?
8. What was the maximum height of the object?

71. 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?
At what time did the object reach its maximum height?
8. What was the maximum height of the object?

72. 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?
What was the maximum height of the object?
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?

73. 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?
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?

74. 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?

75. 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
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?
How long was the object in the air?

76. 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?

77. 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)
How long was the object in the air? Approximately)

78. 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?

79. 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

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

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

82. 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 = 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

83. 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

84. 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 = y2 + 8x – 56 = 0

85. 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

86. 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
x x y2 = 0
(x + 3)2 + y2 - 6x = 0

87. 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 Center = (0, -6) and r = 8
Complete the square in the problems below. Show work!
3. x2 + 22x + 41 = 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 = (x – 5)2 + (y + 9)2 = 256
7. (x + 6)2 + y2 - 20y - 44 = x2 + 20x y2 = 0

88. 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 + y x – 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)

89. 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 (y + 6)2 = x2 + y2 – 12y + 27 = 0

90. 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)

91. 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)

92. 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.

93. 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?

94. 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?

95. 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)

96. 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)

97. 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!

98. 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)

99. 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)

100. 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.)

101. Circles in Standard Form Practice
Write the equation of a circle in standard form for the given information.
1. Center = (0,0) , r = Center = (0, 0), r = 2 7
3 . Center = (2, -5), r =  Center = (-4, 3), r = 62
Center = (0, -8), r = Center = (9, 0), r = 45
Center = (-12, -5), r =  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 = x2 + y2 + 16y = 36
4x2 + 4y2 – 40y = x2 + 54x + 9y2 = 63
x2 – 14x + 7y2 + 56x = x x + 6y2 – 24x = 606

102. 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 = x2 + y2 + 16y – 36 = 0
3. x2 + y2 – 10y = x2 + 6x + y = 0
5. x x + y = x2 + y2 + 28y + 96 = 0
x2 – 2x (y + 4)2 = (x - 6)2 + y2 – 16y = 0
9. (x + 5)2 + y2 – 14y + 13 = x x – 96 + (y – 9)2 = 0
11. (x – 12)2 + y2 + 4y - 5 = x x (y + 3)2 = 0

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

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

105. Parallel Lines cut by a Transversal Practice3 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 Same Side Interior
3. Vertical Angles Alternate Interior
5. Corresponding 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, < <7, <3
9. <3,< <2, <7
11. <1, < <6, <8
13. <4, < <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. < < 1
17. < <2
19. < 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

106. Parallel Lines cut by a Transversal Extra Practice4 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 Same Side Interior
3. Vertical Angles Alternate Interior
5. Corresponding 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, < <6, <3
9. <3,< <2, <7
11. <8, < <7, <8
13. <3, < <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. < < 1
17. < <2
19. < 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

107. 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

108. 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

109. 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

110. 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

111. 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