Free Algebra Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Higher Degree Polynomial Functions

A Polynomial Function is a function of the form:

f(x) = an xn + an - 1 xn - 1+ an - 2 xn - 2 + ... + a1 x + a0

where the a's are real numbers and n is a non-negative integer.

Domains: (-∞, ∞)

Ranges: vary

Degree of a polynomial function is n.

The GRAPHS of polynomial functions are smooth, continuous curves, with no sharp turns.

Cubic Functions are third degree polynomial functions.

The turning points are called Local Extreme Points, or Local Extrema.

Sometimes we are interested in finding the highest or lowest point on the graph of a function over a certain interval. These points are called absolute maximum or absolute minimum points

For example, if we graphed the cubic function f(x) = -3x3 + 8x2 over the interval [ -0.5, 3], this is what we would get: Quartic Functions are fourth degree polynomial functions.

In general, we can tell certain things about polynomial functions just from looking at their equations. We can tell the maximum possible number of x-intercepts and turning points.

For an nth degree polynomial function:

The maximum number of x-intercepts is n.

The maximum number of turning points is n - 1.

We can also tell about the end behavior of polynomial functions. A cubic function will have ends that go in opposite directions, while a quartic function will have ends that either both go up or both go down. The leading coefficient determines the end behavior.

 Function Possible Graphs Degree Turning points End Behavior Degree Even or Odd possitive leading coefficient negative leading coefficient Linear Positive slope Negative slope 1 0  odd Quadratic Possitive leading coefficient Negative leading coefficient 2 1  even Cubic Positive leading coefficient Negative leading coefficient 3 2 or 0  odd Quartic Positive leading coefficient Negative leading coefficient 4 3 or 1  even