Graphing Polynomials
A polynomial is an expression that contains two or more terms. You are likely familiar with graphing quadratic polynomials (y = x2 + 2x + 3). Graphing polynomials with a power greater than 2 becomes a little more complicated.
Finding the Zeros
Multiplicity of Zeros
Rules of Multiplicity
End Behavior
End Behavior Rules
Graphing a Polynomial
- Plot the zeros.
- Sketch the end behavior.
- Apply the rules of multiplicity to the zeros on the leftmost and rightmost sides of the graph, and continue inward until each zero is graphed.
- Connect the lines to complete the sketch.
Plot the zeros
Sketch the end behavior
Apply the rules of multiplicity
Connect the Lines
Rational Roots Test
What happens when the polynomial is not factored?
While quadratics are pretty easy to factor, if you have a polynomial with a large degree, it may be difficult to determine the factors, or even which factor to take out first.
We can use the rational root test to find potential factors of the polynomial.
Practice Problems
Answers to Practice Questions
- 2
- C
- B
- 12
- -2, 0, 7
