Polynomial Functions
Terms and Formulae
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
x
0
in a polynomial.
Degree
-
The value of
n
in a polynomial
f (x) = a
n
x
n + a
n-1
x
n-1 + ... + a
1
x + a
0
, where
a
n≠ 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
a
n
in a polynomial
f (x) = a
n
x
n + a
n-1
x
n-1 + ... + a
1
x + a
0
, where
a
n≠ 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
a
n
x
n + a
n-1
x
n-1 + ... + a
2
x
2 + a
1
x + a
0
, where
a
n, a
n-1,..., a
1, a
0
are real numbers,
n
is a nonnegative integer, and
a
n≠ 0
.
Polynomial Function
-
A function that is defined by a polynomial;
it is of the form
f (x) = a
n
x
n + a
n-1
x
n-1 + ... + a
2
x
2 + a
1
x + a
0
, where
a
n, a
n-1,…, a
1, a
0
are real numbers,
n
is a
nonnegative integer, and
a
n≠ 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) = a
n
x
n + a
n-1
x
n-1 + ... + a
2
x
2 + a
1
x + a
0.
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
a
0
and the denominator of the root is a
factor of
a
n
.
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
ax
2 + bx + c = 0
, then
x = 
.
|
