The problem involves finding specific values on the graph of the function $h(x)$.

Let's examine the requirements:

1. For part (a): Find $h(-2)$.

   • To find $h(-2)$, look at the point where $x = -2$ on the graph and read the corresponding $y$-value.
   • Observing the graph, when $x = -2$, the $y$-value appears to be 4.
   • Therefore, $h(-2) = 4$.

2. For part (b): Find one value of $x$ for which $h(x) = -5$.

   • To solve this, look for the point on the graph where the $y$-value is $-5$.
   • Observing the graph, it appears that when $x = 0$, $y = -5$.
   • So, one value of $x$ for which $h(x) = -5$ is 0.

Final Answers:

• (a) $h(-2) = 4$
• (b) One value of $x$ for which $h(x) = -5$ is $x = 0$.

Would you like further explanation on how these values were derived from the graph?

Here are 5 related questions to deepen understanding:

1. What does it mean for a function value $h(x)$ to be positive or negative on a graph?
2. How can you determine if a function is increasing or decreasing from its graph?
3. What is the significance of the vertex of a parabola in a function's graph?
4. How can we identify the range of a function from its graph?
5. What other values of $x$ could result in the same function output $h(x) = -5$ if the graph had additional intersections?

Tip: When analyzing graphs, always check for symmetry or patterns that can simplify finding specific values.