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.
-7
-5
-3
-1
1
3
5
7
-8
-6
-4
-2
2
4
6
8
x
y

A coordinate system has a horizontal x-axis labeled from negative 7 to 7 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. From left to right, a curve rises at a decreasing rate crossing the x dash axis at negative 3.5 to a maximum comma falls at an increasing rate to the point left parenthesis 0 comma 1 right parenthesis comma rises at an increasing rate to a maximum comma and falls at an increasing rate crossing the x dash axis at 3.5.
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Question content area right
Part 1
​(a) The​ x-intercepts are
  
enter your response here.
​(Use a comma to separate answers as needed. Type an integer or a​ decimal.)
Part 2
​(b) What is the sign of the leading​ coefficient?
Positive
Positive
Negative
Negative
Part 3
​(c) What is the nature of the polynomial whose graph is shown in the​ figure?

Answer 1

Based on the information you've provided about the graph, here are the answers:

Part 1: x-intercepts
The x-intercepts are the points where the graph crosses the x-axis. You mentioned that the curve crosses the x-axis at approximately -3.5 and 3.5. Therefore, the estimated x-intercepts are:
Answer: -3.5, 3.5

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Part 2: Leading Coefficient Sign
The graph rises to the left and falls to the right, which typically indicates that the leading coefficient is negative (for a polynomial with an even degree). Based on this behavior, the sign of the leading coefficient is:
Answer: Negative

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Part 3: Nature of the Polynomial
You mentioned that the graph has a structure with rising and falling behavior that is consistent with either cubic or quartic functions. Since the graph has two x-intercepts (it crosses the x-axis twice) and has peaks and valleys, it supports a quartic nature (fourth degree). Therefore, the polynomial function can be classified as:
Answer: Quartic

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