Graphing Polynomials

Graphing polynomials begins with finding the x-intercepts, or roots, of the function. Take y=(x+1)(x-2)². First set y= to zero and find what values for x satisfies that. If either term equals zero, we know that the product of the two terms will equal zero. So if x=-1 or x=2, y will equal zero. We now can sketch the x-intercepts. Now, let’s think about end behavior of the polynomial. Since it is a third degree polynomial (the parent function is x^3), we know that as x becomes more and more negative, y also becomes more negative. And as x becomes a large positive value, so does y. This allows us to sketch the graph beyond it’s x-intercepts:



Now that we know the x-intercepts and end behavior, let’s finish up by finding the y-intercept. We know the function will intercept the y-axis when x=0, so let’s plug in 0 for x. When x=0, y=4, so that’s our y-intercept, and now we can complete our sketch of the function: