Questions: Plot the y-intercept and the roots. Click on the graph to plot a point. Click a point to delete it.

Plot the y-intercept and the roots. Click on the graph to plot a point. Click a point to delete it.
Transcript text: Plot the $y$-intercept and the roots. Click on the graph to plot a point. Click a point to delete it.
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Solution

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Solution Steps

Step 1: Identify the roots and y-intercept from the sign table.

The sign table shows roots at x = -5 and x = 1. It also indirectly tells us that the y-intercept is negative since at x = 0, the table indicates a negative value.

Step 2: Plot the roots and y-intercept.

The roots are plotted at (-5, 0) and (1, 0). A point on the negative part of the y-axis representing the y-intercept needs to be plotted as well. This will appear below the x-axis, for example, the given prompt has pre-plotted the point (0,-30). However, because the graph does not represent a specific equation, the actual y-intercept value is unknown, and clicking anywhere along the negative y-axis constitutes a correct answer.

Step 3: Connect the points with a curve.

Since the sign chart doesn't specify the degree of the polynomial, there are numerous ways to correctly connect the points, such as by drawing a parabola.

Final Answer:

Plot the points (-5,0), (1,0) and a point below the x-axis, such as (0,-30). You can then connect these with a parabola opening upwards. As no equation is provided, there are several correct parabolic graphs opening either upwards or downwards.

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