https://file.aiquickdraw.com/mathbot/file/1727316558362z6e4hu3f.jpg

Let's analyze the graph to solve the problem based on the provided image:

### Part (a): Evaluate \( f(0) \)
- From the graph, locate the point where \( x = 0 \). This is the y-intercept of the function.
- At \( x = 0 \), the value of \( f(0) = 1 \), which matches the provided answer.

### Part (b): Solve for \( f(x) = -2 \)
- We need to find the \( x \)-values where the function equals \( -2 \) (i.e., the function intersects the horizontal line \( y = -2 \)).
- By inspecting the graph, we can see that the curve touches the line \( y = -2 \) at two points:
  1. One negative \( x \)-value (around \( x = -3 \)).
  2. One positive \( x \)-value (around \( x = 2 \)).

So the solutions for \( f(x) = -2 \) are approximately:
- \( x \approx -3 \)
- \( x \approx 2 \)

Since the problem asks for the larger number first:
- First box: \( 2 \)
- Second box: \( -3 \)

Would you like further details or help with another question?

### Related Questions:
1. How do you find the zeros of a function from its graph?
2. What is the y-intercept of a polynomial function, and why is it important?
3. What can you infer about the behavior of a polynomial function by analyzing its turning points?
4. How do you identify intervals where a function is increasing or decreasing from its graph?
5. What role do inflection points play in understanding the concavity of a function?

**Tip:** When solving equations graphically, always pay attention to the scale of the graph to ensure accuracy in reading values.

Evaluate f(0), and solve for f(x) = -2 based on the given graph. If there are multiple solutions for f(x) = -2, input the larger number first.

Explore how to evaluate the function at zero and solve for f(x) = -2 using a graphical representation. This detailed guide helps students understand function evaluation and graph analysis, essential for high school mathematics.

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