Step-by-step explanation:
How to Graph Polynomials
Plot the x– and y-intercepts on the coordinate plane. ...
Determine which way the ends of the graph point. ...
Figure out if the graph lies above or below the x-axis between each pair of consecutive x-intercepts by picking any value between these intercepts and plugging it into the function.
The graph of a polynomial function will touch the x-axis at zeros with even multiplicities. The graph will cross the x-axis at zeros with odd multiplicities. The sum of the multiplicities is the degree of the polynomial function.
Identify the x-intercepts of the graph to find the factors of the polynomial. Examine the behavior of the graph at the x-intercepts to determine the multiplicity of each factor. Find the polynomial of least degree containing all of the factors found in the previous step.
