5-5: Quadratic Equations Essential Question: How is factoring used to solve quadratic equations?

5-5: Quadratic Equations The standard form of a quadratic equation is: ax2 + bx + c = 0 We can solve some quadratic equations by factoring We’ll solve non-factorable equations after we come back from break We solve a factored quadratic equation because of the Zero-Product Property If ab = 0, then a = 0 or b = 0 Example: If (x + 3)(x – 7) = 0, then x = -3 or x = 7 Take each parenthesis, set it equal to 0 and solve for x

5-5: Quadratic Equations Solve by factoring 2x2 – 11x = -15 Get everything equal to 0 (add 15 to both sides) 2x2 – 11x + 15 = 0 Last step: Set each parenthesis = 0 and solve (next slide) + 2 numbers to: multiply = 30 add = -11 -5 & -6 2x2 x x + 15 -5 -6 x(2x - 5) -3(2x - 5) (x - 3)(2x - 5)

5-5: Quadratic Equations x – 3 = 0 +3 +3 x = 3 2x – 5 = 0 +5 +5 2x = 5 2 2 x = 5/2 Optionally: Check your answers 2x2 – 11x + 15 = 0 2(3)2 – 11(3) + 15 = 0 18 – 33 + 15 = 0 0 = 0 2(5/2)2 – 11(5/2) + 15 = 0 25/2 – 55/2 + 15 = 0

5-5: Quadratic Equations Solve each equation by factoring x2 + 7x = 18 2x2 + 4x = 6 16x2 = 8x x = 2 or x = -9 x = 1 or x = -3 x = 0 or x = ½

5-5: Quadratic Equations Assignment Page 270 1 – 10 (all problems) Solve all problems by factoring (not square roots) No work = no credit