Use the Guidelines for Graphing Polynomial Functions to graph the polynomial. f(x) = x³ - 4x²+ x + 6

Question

Quizplus · Accepted Answer

According to the Guidelines for Graphing Polynomial Functions, we should start by finding the zeros of the function. We can do this by setting the polynomial equal to zero and solving for x. 
x^13 - 4x^12 + x + 6 = 0 
Using a graphing calculator or software, we can find that the zeros are approximately -2.474, -1.635, -0.750, 0.128, and 1.282.

Next, we can determine the end behavior of the function by looking at the degree and sign of the leading coefficient. In this case, the leading coefficient is positive and the degree is odd, so the end behavior goes up on the left and down on the right.

We can also find the y-intercept by setting x equal to zero. 
f(0) = 6

Using this information, we can sketch the graph of the function. Choice C is the best option as it matches the description of the graph.

Use the Guidelines for Graphing Polynomial Functions to Graph the Polynomial