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The Quadratic Formula Notes - The Quadratic Formula When...

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The Quadratic Formula When solving a Quadratic Equation our first choice is using factoring. But if we can not factor the quadratic equation then we need to rely on the Quadratic Formula. The Quadratic Formula: The solutions of the quadratic equation + + 2 , 0, ax bx c a are - ± - = 2 4 2 b b ac x a To solve a Quadratic Equation using the Quadratic Formula….. 1. Write the quadratic equation in standard form, + + 2 , 0, ax bx c a and determine the numerical values of a, b, and c. 2. Substitute the values for a, b, and c into the quadratic formula and then evaluate the formula to obtain the solution. Example 1: Solve the equation + - = 2 2 8 0 x x by using the quadratic formula. Solution: In this equation = = 1, 2, a b and = - 8 c . Using the quadratic formula, - ± - - = 2 2 2 4(1)( 8) 2(1) x - ± + = 2 4 32 2 x - ± = 2 36 2 x - ± = 2 6 2 x - + = 2 6 2 x or - - = 2 6 2 x = = 4 2 2 x or - = = - 8 4 2 x A check will show that both x = 2 and x = -4 are solutions to the equation. Notice that the solutions to the equation + - = 2 2 8 0 x x are two real numbers.
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