Quadratic Expression
An expression including a variable raised to the second power (and no higher powers). Commonly of the form ax^2 + bx + c, where a, b, and c are constants.
FOIL
First, Outside, Inside, Last; an acronym to remember the method for converting from factored to distributed form in a quadratic equation. (x + 2)(x - 3) is a quadratic equation in factored form. Multiply the First, Outside, Inside, and Last terms to get the distributed form. x * x = x^2, x * - 3 = -3x, x * 2 = 2x, and 2 * -3 = -6. The full distributed form is x^2 – 3x + 2x - 6. That can be simplified to x^2 –x - 6.
Undefined
A term describing a situation in which the denominator of a fraction is zero.
Special Products
i. x^2 – y^2 = (x + y)(x - y)
ii. x^2 + 2xy + y^2 = (x + y)(x + y)
iii. x^2 –2xy + y^2 = (x - y)(x - y)
Quadratic Formula
For any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c, are constants, the solutions for x are given by the following equation.
Discriminant
SQRT(b^2 – 4ac). A portion of the quadratic formula that indicates the number of solutions to the given quadratic equation. If the number under the square root sign is positive, there are two solutions to the equation. If the number under the square root sign is zero, there is one solution. If the number under the square root sign is negative, there are zero solutions. Again, the quadratic formula, and thus the discriminant, is seldom tested on the GMAT.
