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9.4 factoring to solve quadratic equations.

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What are the roots of a quadratic function? Roots (x-intercepts): x values when y = 0 ( ___, 0) How do you find the roots for y = x 2 + 5x + 6? 1. Create a table of values 2. Graph the equation 3. Find x when y = 0 Solve: x 2 + 5x + 6 = 0 (-3, 0) and (-2, 0)

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Zero Product Rule 4 9 6 (x + 2) (x + 3)1 36 2 18 3 12 1 6 2 3 0x 2 + 5x + 6366 If ab = 0, then a or b must be 0. y = x 2 + 5x + 6 x 2 + 5x + 6 = 0 (x + 2)(x + 3) = 0 x + 2 = 0 x = -2 x + 3 = 0 x = -3 OR Roots of x 2 + 5x + 6 are (-2, 0) and (-3, 0). List the factors of each. Find the roots of:

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Find the roots for the following. y = (x + 2)(x – 4) (x + 2)(x – 4) = 0 x + 2 = 0 x = -2 x – 4 = 0 x = 4 OR y = (5x + 12)(x – 7) (5x + 12)(x – 7) = 0 5x + 12 = 0 5x = -12 x = -2.4 x – 7 = 0 x = 7 OR y = x(x + 5) x(x + 5) = 0 x = 0x + 5 = 0 x = -5 OR

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Find the roots for the following. 0 = x 2 + 8x + 15 x 2 + 8x + 15 = 0 (x + 3)(x + 5) = 0 x + 3 = 0 x = -3 x + 5 = 0 x = -5 OR x 2 – 5x = 14 x 2 – 5x – 14 = 0 (x + 2)(x – 7) = 0 x + 2 = 0 x = -2 x – 7 = 0 x = 7 OR

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a= b= c= 3 7 6 7 1 6 Find 2 numbers that: Multiply ac Add up to b: 2 Factor pairs of 6 1,6 2,3 (3x + 1)(x + 2) = 0 3x + 1 = 0 x + 2 = 0 3x = -1 x = -2

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Assignment: 9.4 Pg 571: 8-25, 29-33 Skip: 17-19, 24, 32-33 (ignore roster form directions for 29-31)

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a= b= c= 3 7 6 7 1 6 Find 2 numbers that: Multiply ac Add up to b: 2 +6x +2 x(3x +1) + + 2(3x + 1) (3x + 1) (x + 2) + x (6x + 2) Factor pairs of 6 1,6 2,3 (3x + 1)(x + 2) = 0 3x + 1 = 0 x + 2 = 0 3x = -1 x = -2

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