Polynomial and Rational Functions Vocabulary

F(x) = a(x - h)² + k

F(x) = ax² + bx + c

Vertical line over which a parabola is symmetric

An inequality that involves a quadratic polynomial

If R is th eremainder when a polynomial P(x) is divided by x - c, the R = P(c)

An algorithm for dividing a polynomial by (x + a) or (x - a)

The number c is a zero of the polynomial function y = P(x) if and only if x - c is a facor of the polynomial P(x)

If f(x) is a polynomial function with integral coefficients and p/q is a rational zero of f(x) the p is a factor of the constant term and q is a factor of the leading coefficient

The number of times a root occurs in the complete factorization of a polynomial

Suppose P(x) = 0 is a polynomial equation with real coefficients and with terms written in descending order. Then,

• the number of positive real roots of the equation is either equal to the number of sign variation of P(x) or is less than that by an even integer
• the number of negative real roots ot he equation is either equal to the number of sign variations of P(-x) or is less than that by an even integer

Suppose that P(x) is a polynomial with real coefficients and a positive leading coefficient and synthetic division with x - c is performed.

• If c > 0 and all terms in the bottom row are nonnegative, then c is an upper bound for the roots of P(x) = 0
• If c < 0 and the terms in the bottom row alternate in sign, the c is a lower bound for the roots of P(x) = 0

A function of the form where P(x) and Q(x) are polynomials

Vertical or horizontal line which the curve gets closer and closer to but never touches

The statement y varies directly as x means that y = kx for some fixed nonzero real number k. Direct variation is a situation in which as one quantity increases, the other increases at a constant rate.

The statement y varies inversely as x means that y = for some fixed nonzero real number k.Inverse variation is a situation in which as one quantity increases, the other decreases at a constant rate.