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!