2. Objective: Use factoring to solve quadratic equations. Standard(s) being met: 2.8 Algebra and Functions

3. Steps for solving a quadratic equation: 3x 2 - 3x = 18 1.) Set the equation equal to zero. 3x 2 – 3x – 18 = 0 2.) Completely factor the quadratic expression. 3(x 2 – x – 6) = 0 3(x – 3)(x + 2) = 0 3.) Set any factor that contains a variable equal to zero and solve for the variable. x – 3 = 0 x = 3 x + 2 = 0 x = -2

4. 4.) Check your solutions by substituting each of them for the variable in the original equation. 3x 2 – 3x = 18 3(3 2 ) – 3(3) = 18 3 · 9 – 9 = 18 27 – 9 =18 18 = 18 3(-2) 2 – 3(-2) = 18 3 · 4 – (-6) = 18 12 + 6 = 18 18 = 18, So the solutions to 3x 2 -3x = 18 are 3 and -2.

5. Ex. 1, Solve each quadratic equation. a.) 15x 2 – 93x = -18 15x 2 – 93x + 18 = 0 3(5x 2 – 31 x + 6) = 0 3(x – 6)(5x -1) = 0 x – 6 = 0, x = 6 5x – 1 = 0 5x = 1 x = 1/5 x = 6, 1/5

6. Ex. 1, Solve each quadratic equation.  a.) 15x 2 – 93x = -18  b.) 128x 3 = 98x  c.) 6x 2 – 4 = 5x  d.) 12x 2 – 8x – 13 = 2  e.) 2x 2 + 3x - 20 = 7 – 2x 2

7. b.) 128x 3 = 98x 128x 3 - 98x = 0 2x(64x 2 – 49) = 0 2x(8x + 7)(8x – 7) = 0 2x = 0 x =0 8x + 7 = 0 x = -7/8 8x – 7 = 0 x = 7/8 x = 0, -7/8, 7/8

8. c.) 6x 2 – 4 = 5x 6x 2 – 5x – 4 = 0 (2x + 1)(3x – 4) = 0 2x + 1 = 0 2x = -1 x = -1/2 3x – 4 = 0 3x = 4 x = 4/3 x = -1/2, 1 1/3

9. d.) 12x 2 – 8x – 13 = 2 12x 2 – 8x -15 = 0 (6x + 5)(2x – 3) = 0 6x + 5 = 0 6x = -5, x = -5/6 2x – 3 = 0 2x = 3, x = 3/2 x = -5/6, 1 ½ x = -5/6, 1 ½ e.) 2x 2 + 3x - 20 = 7 – 2x 2 4x 2 + 3x – 27 = 0 (4x - 9)(x + 3) = 0 4x – 9 = 0 4x = 9, x = 9/4 x + 3 = 0 x = -3 x = 2 ¼, -3

10. Do page 146 together. Do page 145 on your own.