To determine which graph could represent Tempestt’s function with a maximum at (-4, 2), let’s consider the following key points:

1. Characteristics of a Maximum

Points (-4, 2) are the highest points on the graph.
This means the graph reaches its peak at (-4, 2) and decreases on both sides of this point.

2. Function Type

• If the function is a quadratic (parabola), the graph will open downward since it has a maximum.
• A general form for such a quadratic function is f(x)=a(x+4)2+2f(x)=a(x+4)2+2, where a<0a<0.

3. Vertex Form

• The function’s vertex, (−4,2)(−4,2), indicates that the graph is symmetric around x=−4x=−4, and the y-coordinate at this vertex is 22.

4. Possible Graph Description

• The graph passes through (−4,2)(−4,2) and declines on either side of x=−4x=−4.
• It should have a peak at this point, whether it is part of a parabola or another function with a maximum (like a sine curve in some cases).

5. Examples of Equations

• A quadratic function: f(x)=−2(x+4)2+2f(x)=−2(x+4)2+2.
• A cubic function: f(x)=−x3−4×2+6f(x)=−x3−4×2+6, though less common for this case.
• A sine function (if periodic): f(x)=2+sin⁡(x+4)f(x)=2+sin(x+4), though this would have multiple peaks and valleys.

Which Could Be Her Graph?

If you are provided with specific graphs, look for the one:

• Peaks at (-4, 2).
• Decreases symmetrically on both sides of x=−4x=−4 if it’s a parabola.
• Does not rise above y = 2 anywhere else.

Share any options if you’d like help selecting!

In Summary

Tempestt’s graph must have:

1. A maximum at $(-4,2)$, meaning the graph peaks at this point.
2. Symmetry around $x=-4$ (if it’s a parabola).
3. A downward slope on both sides of $x=-4$ (if it’s a quadratic or similar function).

Look for a graph that meets these criteria.

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