Splash Screen.

Slides:



Advertisements
Similar presentations
Name:__________ warm-up 4-3 Use the related graph of y = –x 2 – 2x + 3 to determine its solutions Which term is not another name for a solution to a quadratic.
Advertisements

Splash Screen. Then/Now I CAN solve radical equations. Learning Target.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–5) CCSS Then/Now New Vocabulary Key Concept: Quadratic Formula Example 1:Two Rational Roots.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–4) CCSS Then/Now New Vocabulary Key Concept: The Quadratic Formula Example 1:Use the Quadratic.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–4) CCSS Then/Now New Vocabulary Example 1:Use the Distributive Property Key Concept: Factoring.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–2) CCSS Then/Now New Vocabulary Example 1: The Distributive Property Key Concept: FOIL Method.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–5) CCSS Then/Now New Vocabulary Key Concept: Factoring x 2 + bx + c Example 1:b and c are.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–3) CCSS Then/Now New Vocabulary Key Concept: Power Property of Equality Example 1:Real-World.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–6) CCSS Then/Now New Vocabulary Example 1:Write Functions in Vertex Form Example 2:Standardized.
Perfect Squares Lesson 8-9 Splash Screen.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–2) CCSS Then/Now New Vocabulary Key Concept: FOIL Method for Multiplying Binomials Example.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–8) CCSS Then/Now New Vocabulary Key Concept: Factoring Perfect Square Trinomials Example 1:
Splash Screen. Example 1 Write an Equation Given Roots (x – p)(x – q)=0Write the pattern. Simplify. Replace p with and q with –5. Use FOIL.
Splash Screen. Lesson Menu Five-Minute Check (over Chapter 8 ) CCSS Then/Now New Vocabulary Key Concept: Quadratic Functions Example 1: Graph a Parabola.
Over Lesson 8–5 A.A B.B C.C D.D 5-Minute Check 1 (x + 11)(x – 11) Factor x 2 – 121.
Splash Screen. Over Lesson 8–4 5-Minute Check 1 A.16x B. 16x x + 25 C. 16x x + 25 D. 4x x + 5 Find (4x + 5) 2.
Splash Screen.
Splash Screen. Then/Now You solved quadratic equations by completing the square. Solve quadratic equations by using the Quadratic Formula. Use the discriminant.
Questions on Practice Assignment? Page , 23, 33, 41 Page 263, ,
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–4) CCSS Then/Now New Vocabulary Example 1:Use the Distributive Property Key Concept: Factoring.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–2) CCSS Then/Now New Vocabulary Key Concept: FOIL Method for Multiplying Binomials Example.
Splash Screen. Concept Example 1 Translate Sentences into Equations (x – p)(x – q)=0Write the pattern. Simplify. Replace p with and q with –5. Use FOIL.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–4) CCSS Then/Now New Vocabulary Example 1:Equation with Rational Roots Example 2:Equation.
Splash Screen.
Splash Screen.
Splash Screen.
Section 4.3 Notes: Solving Quadratic Equations by Factoring
Graphing Quadratic Functions Solving by: Factoring
LESSON 8–7 Solving ax2 + bx + c = 0.
Splash Screen.
Quadratic Expressions and Equations
WS Countdown: 9 due today!
A B C D Solve x2 + 8x + 16 = 16 by completing the square. –8, 0
5-3 Solving Quadratic Equations by Graphing and Factoring Warm Up
LESSON 8–6 Solving x2 + bx + c = 0.
Splash Screen.
Splash Screen.
Solve 25x3 – 9x = 0 by factoring.
Splash Screen.
A B C D Use the Distributive Property to factor 20x2y + 15xy.
Splash Screen.
Five-Minute Check (over Lesson 3–4) Mathematical Practices Then/Now
Solve a quadratic equation
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Complete the Square Lesson 1.7
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Splash Screen.
Factor the equation: 3
Splash Screen.
Splash Screen.
Splash Screen.
Example 1 Write an Equation Given Slope and a Point
You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations.
Splash Screen.
Splash Screen.
David threw a baseball into the air
Factor the equation:
Presentation transcript:

Splash Screen

Mathematical Practices 2 Reason Abstractly and quantitatively. Content Standards A.SSE.2 Use the structure of an expression to identify ways to rewrite it. F.IF.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Mathematical Practices 2 Reason Abstractly and quantitatively. CCSS

You found the greatest common factors of sets of numbers. Write quadratic equations in intercept form. Solve quadratic equations by factoring. Then/Now

factored form FOIL method Vocabulary

Concept

(x – p)(x – q) = 0 Write the pattern. Translate Sentences into Equations (x – p)(x – q) = 0 Write the pattern. Replace p with and q with –5. Simplify. Use FOIL. Example 1

Multiply each side by 2 so b and c are integers. Translate Sentences into Equations Multiply each side by 2 so b and c are integers. Answer: Example 1

A. ans B. ans C. ans D. ans Example 1

Concept

9y 2 + 3y = 0 Original equation 3y(3y) + 3y(1) = 0 Factor the GCF. Factor GCF A. Solve 9y 2 + 3y = 0. 9y 2 + 3y = 0 Original equation 3y(3y) + 3y(1) = 0 Factor the GCF. 3y(3y + 1) = 0 Distributive Property 3y = 0 3y + 1 = 0 Zero Product Property y = 0 Solve each equation. Answer: Example 2

5a 2 – 20a = 0 Original equation 5a(a) – 5a(4) = 0 Factor the GCF. Factor GCF B. Solve 5a2 – 20a = 0. 5a 2 – 20a = 0 Original equation 5a(a) – 5a(4) = 0 Factor the GCF. 5a(5a – 4) = 0 Distributive Property 5a = 0 a – 4 = 0 Zero Product Property a = 0 a = 4 Solve each equation. Answer: 0, 4 Example 2

Solve 12x – 4x2 = 0. A. 3, 12 B. 3, –4 C. –3, 0 D. 3, 0 Example 2

x 2 = (x)2; 9 = (3)2 First and last terms are perfect squares. Perfect Squares and Differences of Squares A. Solve x 2 – 6x + 9 = 0. x 2 = (x)2; 9 = (3)2 First and last terms are perfect squares. 6x = 2(x)(3) Middle term equals 2ab. x 2 – 6x + 9 is a perfect square trinomial. x 2 + 6x + 9 = 0 Original equation (x – 3)2 = 0 Factor using the pattern. x – 3 = 0 Take the square root of each side. x = 3 Add 3 to each side. Answer: 3 Example 3

y2 – 36 = 0 Subtract 36 from each side. Perfect Squares and Differences of Squares B. Solve y 2 = 36. y 2 = 32 Original equation y2 – 36 = 0 Subtract 36 from each side. y2 – (6)2 = 0 Write in the form a2 – b2. (y + 6)(y – 6) = 0 Factor the difference of squares. y + 6 = 0 y – 6 = 0 Zero Product Property y = –6 y = 6 Solve each equation. Answer: –6, 6 Example 3

A. Solve x 2 – 2x – 15 = 0. ac = –15 a = 1, c = –15 Factor Trinomials Example 4

x 2 – 2x – 15 = 0 Original equation Factor Trinomials x 2 – 2x – 15 = 0 Original equation x2 + mx + px – 15 = 0 Write the pattern. x 2 + 3x – 5x – 15 = 0 m = 3 and p = –5 (x 2 + 3x) – (5x + 15) = 0 Group terms with common factors. x(x + 3) – 5(x + 3) = 0 Factor the GCF from each grouping. (x – 5)(x + 3) = 0 Distributive Property x – 5 = 0 x + 3 = 0 Zero Product Property x = 5 x = –3 Solve each equation. Answer: 5, –3 Example 4

B. Solve 5x 2 + 34x + 24 = 0. ac = 120 a = 5, c = 24 Factor Trinomials Example 4

5x 2 + 34x + 24 = 0 Original equation Factor Trinomials 5x 2 + 34x + 24 = 0 Original equation 5x2 + mx + px + 24 = 0 Write the pattern. 5x 2 + 4x + 30x + 24 = 0 m = 4 and p = 30 (5x 2 + 4x) + (30x + 24) = 0 Group terms with common factors. x(5x + 4) + 6(x + 4) = 0 Factor the GCF from each grouping. (x + 6)(5x + 4) = 0 Distributive Property x + 6 = 0 5x + 4 = 0 Zero Product Property x = –6 Solve each equation. Example 4

Factor Trinomials Answer: Example 4

B. Factor 3s 2 – 11s – 4. A. (3s + 1)(s – 4) B. (s + 1)(3s – 4) C. (3s + 4)(s – 1) D. (s – 1)(3s + 4) Example 4

Solve Equations by Factoring ARCHITECTURE The entrance to an office building is an arch in the shape of a parabola whose vertex is the height of the arch. The height of the arch is given by h = 9 – x 2, where x is the horizontal distance from the center of the arch. Both h and x are measured in feet. How wide is the arch at ground level? To find the width of the arch at ground level, find the distance between the two zeros. Example 5

9 – x 2 = 0 Original expression x 2 – 9 = 0 Multiply both sides by –1. Solve Equations by Factoring 9 – x 2 = 0 Original expression x 2 – 9 = 0 Multiply both sides by –1. (x + 3)(x – 3) = 0 Difference of squares x + 3 = 0 or x – 3 = 0 Zero Product Property x = –3 x = 3 Solve. Answer: The distance between 3 and – 3 is 3 – (–3) or 6 feet. Example 5

Check 9 – x 2 = 0 9 – (3)2 = 0 or 9 – (–3)2 = 0 9 – 9 = 0 9 – 9 = 0 Solve Equations by Factoring Check 9 – x 2 = 0 9 – (3)2 = 0 or 9 – (–3)2 = 0 ? 9 – 9 = 0 9 – 9 = 0 ? 0 = 0 0 = 0   Example 5

TENNIS During a match, Andre hit a lob right off the court with the ball traveling in the shape of a parabola whose vertex was the height of the shot. The height of the shot is given by h = 49 – x 2, where x is the horizontal distance from the center of the shot. Both h and x are measured in feet. How far was the lob hit? A. 7 feet B. 11 feet C. 14 feet D. 25 feet Example 5

End of the Lesson