# Polynomial Functions

### Contents

#### Terms

Asymptote  -  A line that a function approaches but never intersects.
Axis  -  The line of symmetry of a parabola.
Constant Function  -  A polynomial function of degree zero in which the constant term ≠ 0.
Constant Term  -  The coefficient of x0 in a polynomial.
Degree  -  The value of n in a polynomial f (x) = anxn + an-1xn-1 + ... + a1x + a0, where an≠ 0. If f (x) = 0, then the degree is undefined.
Descartes' Rule of Signs  -  Descartes' Rule of Signs states that the number of positive real roots is less than or equal to the number of variations in the function f (x). It also states that the number of negative real roots is less than or equal to the number of variations in the function f (- x).
Leading Coefficient  -  The value of an in a polynomial f (x) = anxn + an-1xn-1 + ... + a1x + a0, where an≠ 0 unless f (x) = 0.
Linear Function  -  A first-degree polynomial.
Multiplicity  -  If (x - c)n is a factor of a polynomial but (x - c)n+1 is not, the root c is said to be a root of multiplicity n.
Parabola  -  Another name for the graph of a quadratic function.
Polynomial  -  An expression of one variable of the form anxn + an-1xn-1 + ... + a2x2 + a1x + a0, where an, an-1,..., a1, a0 are real numbers, n is a nonnegative integer, and an≠ 0.
Polynomial Function  -  A function that is defined by a polynomial; it is of the form f (x) = anxn + an-1xn-1 + ... + a2x2 + a1x + a0, where an, an-1,…, a1, a0 are real numbers, n is a nonnegative integer, and an≠ 0.
Quadratic Function  -  A second-degree polynomial.
Rational Function  -  A function which can be expressed as the quotient of two polynomial functions.
Rational Root Theorem  -  The Rational Root Theorem is a useful tool in finding the roots of a polynomial function f (x) = anxn + an-1xn-1 + ... + a2x2 + a1x + a0. If the coefficients of a polynomial are all integers, and a root of the polynomial is rational (it can be expressed as a fraction in lowest terms), the Rational Root Theorem states that the numerator of the root is a factor of a0 and the denominator of the root is a factor of an.
Root  -  Values of the independent variable for which a polynomial function equals zero.
Variation  -  Consecutive terms of a polynomial whose coefficients have opposite signs.
Vertex  -  The point on a parabola at which the quadratic function reaches its minimum or maximum value.
Zero Polynomial  -  The polynomial f (x) = 0.

#### Formulae

 Quadratic Formula If ax2 + bx + c = 0, then x = .