Use the given graph of the polynomial function to complete the following.

Question

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.
-10
-8
-6
-4
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y

A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. From left to right, a curve falls steeply at a decreasing rate passing through the point (negative 2, 0) to a local minimum, rises at an increasing rate passing through the points (0, negative 1) and left parenthesis 3 comma 0 right parenthesis to a local maximum comma and falls steeply at an increasing rate passing through the point left parenthesis 6 comma 0 right parenthesis.
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Question content area right
Part 1
a. The​ x-intercepts are xequals
  
enter your response here.
​(Use a comma to separate answers as​ needed.)
Part 2
b. What is the sign of the leading​ coefficient?
Positive
Negative
Part 3
c. What is the nature of the polynomial whose graph is shown in the​ figure?
Cubic
Quartic

Answer 1

Based on the description of the graph of the polynomial function provided:

Part 1

a. The x-intercepts are \( x = -2, 3, 6 \).

• These points are where the graph intersects the x-axis.

Part 2

b. The sign of the leading coefficient is Positive.

• Since the graph falls to the left and rises to the right, it indicates a polynomial with a positive leading coefficient.

Part 3

c. The nature of the polynomial whose graph is shown is Cubic.

• A cubic polynomial will typically have up to 3 real roots (which we see at the x-intercepts) and can have a maximum of two turning points.

Summary of Answers:

a. The x-intercepts are \( x = -2, 3, 6 \).
b. Positive
c. Cubic