Quadratic equations: Quadratic equations Quiz

A quadratic expression is a polynomial such as x² + 6x + 8, in which there is one unknown value raised to the second power (squared) in one of the terms -- generally the first term. If this expression is set equal to zero, as in x² + 6x + 8 = 0, you have a quadratic equation. The first term can have a coefficient other than 1, such as with 2x² + 6x + 8, and the middle term will have x to the first power along with a coefficient. The final term is a known value. Quadratic equations, unlike linear equations, can have two solutions, not just one. On the SAT, factoring the expression into two polynomials will usually be a simple way to solve the equation, so that x² + 6x + 8 = 0 becomes (x + 2)(x + 4) = 0 and we arrive at two solutions: x = -2 and x = -4. You should also be able to work in the opposite direction, by distributing the terms in the factored expression. This can be done using FOIL, multiplying the First terms, Outer terms, Inner terms, and Last terms. The product of the Outer and Inner, which will have like terms, can then be added. When graphed, quadratic equations generally take the shape of a parabola.