https://file.aiquickdraw.com/mathbot/file/1726536709381u20faokz.jpg

Let's analyze the graph step by step to solve the two questions:

### (a) Find \( h(-2) \):
To find \( h(-2) \), we look at the graph and locate where \( x = -2 \). From the graph, at \( x = -2 \), the value of \( h(x) \) corresponds to the point on the y-axis at that position.

Looking closely, at \( x = -2 \), the graph shows that \( h(-2) = 4 \).

Thus, 
\[
h(-2) = 4
\]

### (b) Find one value of \( x \) for which \( h(x) = -5 \):
To find the value of \( x \) for which \( h(x) = -5 \), we need to locate where the graph intersects the line \( y = -5 \).

From the graph, it intersects the line \( y = -5 \) at \( x = -4 \). Thus, one value of \( x \) for which \( h(x) = -5 \) is:
\[
x = -4
\]

### Final Answers:
(a) \( h(-2) = 4 \)

(b) \( x = -4 \) when \( h(x) = -5 \)

Would you like more details or further explanation?

Here are 5 related questions for further exploration:
1. What would \( h(x) \) be for \( x = 0 \)?
2. How can you find the vertex of the parabola from the graph?
3. What is the axis of symmetry of the parabola?
4. Is there any other \( x \)-value for which \( h(x) = -5 \)?
5. How does the graph behave for large positive and negative values of \( x \)?

**Tip:** When analyzing graphs, always check for key points like the vertex, intercepts, and symmetry to gain better insights into the function!

The graph of a function h is shown. Find h(-2) and one value of x for which h(x) = -5.

This problem involves interpreting a graph to find h(-2) and determining the value of x when h(x) = -5. Suitable for students in Grades 7-9 who are learning about quadratic functions and graph analysis.

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