Answer to Question #164655 in Linear Algebra for James Russell

Question

A certain polynomial has a graph which has an end behaviour of II → IV. It has 2 turning points and 1 x-intercept. Sketch the shape of the graph and indicate what degree the polynomial is and whether its leading coefficient is positive or negative.

Answer 1

Answer:

Step 1

Given:

• A polynomial graph has an end behavior of II→IV
• II→IV.
• Two turning points and 1 x-intercept.

The objective is,

1. To sketch the graph and indicate the degree of the polynomial.
2. To find that the leading coefficient is positive or negative.

Step 2

The graph with end behavior of II→IV

II→IV, two turning points and 1 x-intercept will be like,

The obtained graph contains two turning points, then the degree of the polynomial will be 3.

Since, the end behavior is from II→IV

II→IV, it approaches −∞

-∞.

Hence, the degree of the polynomial is 3 and the leading coefficient is negative.