Objective Use factoring to solve quadratic equations Standards
Objective: Use factoring to solve quadratic equations. Standard(s) being met: 2. 8 Algebra and Functions
Steps for solving a quadratic equation: 3 x 2 - 3 x = 18 1. ) Set the equation equal to zero. 3 x 2 – 3 x – 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. ) Check your solutions by substituting each of them for the variable in the original equation. 3 x 2 – 3 x = 18 3(32) – 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 3 x 2 -3 x = 18 are 3 and -2.
Ex. 1, Solve each quadratic equation. a. ) 15 x 2 – 93 x = -18 15 x 2 – 93 x + 18 = 0 3(5 x 2 – 31 x + 6) = 0 3(x – 6)(5 x -1) = 0 x – 6 = 0, x = 6 5 x – 1 = 0 5 x = 1/5 x = 6, 1/5
• b. ) 128 x 3 = 98 x 128 x 3 - 98 x = 0 2 x(64 x 2 – 49) = 0 2 x(8 x + 7)(8 x – 7) = 0 2 x = 0 x =0 8 x + 7 = 0 x = -7/8 8 x – 7 = 0 x = 7/8 x = 0, -7/8, 7/8
Do page 146 together. Do page 145 on your own.
- Slides: 8