The Quadratic Formula
Students learn to solve quadratic equations in the form ax^2 + bx + c = 0 using the quadratic formula, which states that x = -b plus or minus the square root of b^2 - 4ac over 2a. For example, to solve the equation x^2 - 3x - 8 = 0, since a = 1, b = -3, and c = -8, the quadratic formula states that x = 3 plus or minus the square root of (-3)^2 - 4(1)(-8) over 2(1). Simplifying on the right side of the equation, x = 3 plus or minus the square root of 9 + 32 over 2, or x = 3 plus or minus the square root of 41 over 2, which is the final answer. Note that students also learn to derive the quadratic formula using completing the square in the first example problem in this lesson.