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I can use the zero product property to solve quadratics by factoring

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Warm Up Use your calculator to find the x-intercept of each function. 1. f(x) = x 2 - 6x f(x) = -x 2 – 2x + 3 Factor each expression. 3. 3x 2 – 12x4. x 2 – 9x x 2 – 49 3x(x – 4) (x –7)(x +7) (x –6)(x –3)

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Connections We find zeros on a graph by looking at the x-intercepts or viewing the table and identifying the x-intercept as the point where y=0. Using this knowledge determine how one could find the zeros of a quadratic algebraically. Share your method with your partner. Use f(x) = x 2 – 3x – 18 to help your discussion.

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You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations have solutions or roots. Reading Math

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Find the zeros of the function by factoring. Example 2A: Finding Zeros by Factoring f(x) = x 2 – 4x – 12 x 2 – 4x – 12 = 0 (x + 2)(x – 6) = 0 x + 2 = 0 or x – 6 = 0 x= –2 or x = 6 Set the function equal to 0. Factor: Find factors of –12 that add to –4. Apply the Zero Product Property. Solve each equation.

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Find the zeros of the function by factoring. Example 2B: Finding Zeros by Factoring g(x) = 3x x 3x x = 0 3x(x+6) = 0 3x = 0 or x + 6 = 0 x = 0 or x = –6 Set the function to equal to 0. Factor: The GCF is 3x. Apply the Zero Product Property. Solve each equation.

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Check It Out! Example 2a f(x)= x 2 – 5x – 6 Find the zeros of the function by factoring. A. B. g(x) = x 2 – 8x

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Quadratic expressions can have one, two or three terms, such as –16t 2, –16t t, or –16t t + 2. Quadratic expressions with two terms are binomials. Quadratic expressions with three terms are trinomials. Some quadratic expressions with perfect squares have special factoring rules.

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Find the roots of the equation by factoring. Example 4B: Find Roots by Using Special Factors 18x 2 = 48x – 32 Rewrite in standard form. Factor. The GCF is 2. Divide both sides by 2. Write the left side as a 2 – 2ab +b 2. Apply the Zero Product Property. Solve each equation. 18x 2 – 48x + 32 = 0 2(9x 2 – 24x + 16) = 0 (3x – 4) 2 = 0 3x – 4 = 0 or 3x – 4 = 0 x = or x = 9x 2 – 24x + 16 = 0 (3x) 2 – 2(3x)(4) + (4) 2 = 0 Factor the perfect-square trinomial.

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Find the roots of the equation by factoring. Example 4A: Find Roots by Using Special Factors 4x 2 = 25 Rewrite in standard form. Factor the difference of squares. Write the left side as a 2 – b 2. Apply the Zero Product Property. Solve each equation. 4x 2 – 25 = 0 (2x) 2 – (5) 2 = 0 (2x + 5)(2x – 5) = 0 2x + 5 = 0 or 2x – 5 = 0 x = – or x =

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A. x 2 – 4x = –4 Find the roots of the equation by factoring. Check It Out! Example 4a B. 25x 2 = 9

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Write a quadratic function in standard form with zeros 4/3 and –7. Your factors should not include fractions. Example 5: Using Zeros to Write Function Rules

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Check It Out! Example 5 Write a quadratic function in standard form with zeros 5/2 and –5. Your factors should not include fractions.

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Could you develop more than one quadratic with the same zeros? If yes give an example use the zeros 2 and 4. If no explain why.

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