I can use the zero product property to

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

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

Warm Up Use your calculator to find the x-intercept of each function. 1. f(x)

Warm Up Use your calculator to find the x-intercept of each function. 1. f(x) = x 2 - 6 x + 8 2. f(x) = -x 2 – 2 x + 3 Factor each expression. 3. 3 x 2 – 12 x 5. x 2 – 49 3 x(x – 4) 4. x 2 – 9 x + 18 (x – 6)(x – 3) (x – 7)(x +7)

Connections � We find zeros on a graph by looking at the x-intercepts or

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 – 3 x – 18 to help your discussion.

You can find the roots of some quadratic equations by factoring and applying the

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

Example 2 A: Finding Zeros by Factoring Find the zeros of the function by

Example 2 A: Finding Zeros by Factoring Find the zeros of the function by factoring. f(x) = x 2 – 4 x – 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.

Example 2 B: Finding Zeros by Factoring Find the zeros of the function by

Example 2 B: Finding Zeros by Factoring Find the zeros of the function by factoring. g(x) = 3 x 2 + 18 x = 0 3 x(x+6) = 0 3 x = 0 or x + 6 = 0 x = 0 or x = – 6 Set the function to equal to 0. Factor: The GCF is 3 x. Apply the Zero Product Property. Solve each equation.

Check It Out! Example 2 a Find the zeros of the function by factoring.

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

Quadratic expressions can have one, two or three terms, such as – 16 t

Quadratic expressions can have one, two or three terms, such as – 16 t 2, – 16 t 2 + 25 t, or – 16 t 2 + 25 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.

Example 4 B: Find Roots by Using Special Factors Find the roots of the

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

Example 4 A: Find Roots by Using Special Factors Find the roots of the

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

Check It Out! Example 4 a Find the roots of the equation by factoring.

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

Example 5: Using Zeros to Write Function Rules Write a quadratic function in standard

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

Check It Out! Example 5 Write a quadratic function in standard form with zeros

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

Could you develop more than one quadratic with the same zeros? If yes give

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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