5b)++Graphs+of+polynomial+functions

Section 5b will teach and explain how to graph polynomial functions. A polynomial function "is a collection of terms that each consist of a coefficient and a power of x" and looks like: y = 2x⁴ + 4x² - 6x + 3. In order to graph this, you must recognize what the degree of the polynomial is, and what the leading coefficient is. The degree of the polynomial "is the highest power of x", and the leading coefficient "is the coefficient of the term with the highest power of x". In this example, the degree is 4, so the leading coefficient is 2. Also, the constant term, the term without a power of x, is used to create the graph. The number of hills and valleys, direction of the far right and far left of the graph, and the y-intercept can all be determined using the previously stated information.

Example 1: This Graph: Y intercept=8 (constant term: # without a variable) Degree of Polynomial: 4 (highest power) Leading coefficient: -5 (coefficient of term with of highest power) Max # Hills and Valleys: 3 (one less than the degree) Graph Direction Far Left: Down (even degree, 4, so direction matches far right) Graph Direction Far Right: Down (Negative leading coefficient, -5)



The example in the equation above was modified by another wiki team who used the same file name for their work This Graph: Y intercept = 2 Degree of Polynomial: 5 Leading Coefficient: -1 Max # Hills and Valleys: 4 Graph Direction Far Left: Up (odd highest degree) Graph Direction Far Right: Down



Example 3:

The example in the graph above was modified by another wiki team who used the same file name for their work This Graph:

Y-Intercept: 4 Degree of Polynomial: 3 Leading Coefficient: -1 Maximum # of hills and valleys: 2 Graph Direction Far Left: Up (odd highest degree) Graph Direction Far Right: Down

Helpful links:  [] [] Go to the next lesson as well, so you see a complete tutorial

Tutorial: