Question

Use the given graph of the polynomial function to complete the following.a. Estimate the x-intercept(s).b. State whether the leading coefficient is positive or negative.c. Determine whether the polynomial function is cubic or quartic.

Answer 1

(a)

The x-intercepts are the x-axis cutting points.

Looking at the graph, we see that the x-axis cutting points are at:

x = - 2

x = 1

x = 3

So, these are the x-intercepts.

(b)

The leading coefficient is the coefficient of the highest degree term.

Let's look at basic shapes of graphs of positive cubic function, negative cubic function, positive quartic function, and negative quartic function.

Graph shown below:

The graph in your question matches the first graph.

So, we can say

The leading coefficient is positive.

(c)

Looking at the graphs from part (b), we see that the shape of the graph in our question resembles a cubic function.

So,

The graph is cubic.