2.2 Solving Quadratic Equations Algebraically Quadratic Equation: Equation written in the form ax 2 + bx + c = 0 ( where a ≠ 0). Zero Product Property: If a product of real #'s is zero, then at least one of the factors is zero: If ab = 0, then a = 0, b = 0, or both.

Ex. #1 Solve by Factoring. a) x 2 – 8x + 15 = 0 b) 3x 2 + x = 4 c) 12x x = 4

Solving x 2 = k k  0 No solutions k = 0 1 solution k  0 2 solutions Ex. #2 Solve a) x 2 = 9 b) 3x 2 = 12c) 25x 2 – 4 = 0

Ex. #3 Solve Using the quadratic formula: Round to nearest thousandths and give exact answers. 5x 2 + 8x = -2

Discriminant: b 2 – 4ac If the discriminant  0, then there are 2 real solutions. If the discriminant = 0, then there is 1 real solution. If the discriminant  0, then there are 0 real solutions. Ex. #4 How many solutions does each quadratic equation have? a) x 2 + 4x + 1 = 0 b) -9x 2 = 12x + 10

Completing the Square:

Ex. #5 Solve by completing the square. a) x 2 – 8x + 15 = 0 b) 2x 2 – 6x + 1 = 0