https://file.aiquickdraw.com/mathbot/file/1726852613878kvhgz2rd.jpg

Let's analyze the graph and the questions provided.

### Observations from the graph:
- The graph is a parabola that opens upwards with a vertex at the point \((0, -4)\). 
- The graph crosses the x-axis at \((-2, 0)\) and \((2, 0)\), which are the **x-intercepts**.
- The **y-intercept** occurs at \((0, -4)\).

### Answering the questions:

1. **The domain** (part a):
   Since the parabola extends indefinitely in both the left and right directions, the domain is all real numbers.
   - **Answer**: \((-\infty, \infty)\).

2. **The range** (part b):
   The lowest point on the graph (the vertex) is \(-4\), and the parabola opens upwards, so the range starts from \(-4\) and goes to infinity.
   - **Answer**: \([-4, \infty)\).

3. **The x-intercepts** (part c):
   The graph crosses the x-axis at the points \((-2, 0)\) and \((2, 0)\).
   - **Answer**: \(-2, 2\).

4. **The y-intercept** (part d):
   The graph crosses the y-axis at \((0, -4)\).
   - **Answer**: \(-4\).

5. **Missing function values (f(-2) and f(2))** (last part):
   - \( f(-2) = 0 \) and \( f(2) = 0 \), as both points are the x-intercepts, meaning the function equals 0 at these points.

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Let me know if you'd like more details on any part of this or have additional questions.

Here are 5 related questions:
1. How do we determine the vertex of a parabola from its equation?
2. What are the general forms of a quadratic function?
3. How do the domain and range change if the parabola opens downwards?
4. What is the symmetry of the graph of a parabola, and how does it help in solving problems?
5. How do you find the roots of a quadratic equation algebraically?

### Tip:
For quadratic functions, the vertex can be found using the formula \(x = \frac{-b}{2a}\) when the function is in standard form \(ax^2 + bx + c\).

Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks below. f(-2) = ? f(2) = ?

Analyze a quadratic function's graph to determine its domain, range, x-intercepts, y-intercepts, and evaluate missing function values. This lesson is suitable for high school students and focuses on interpreting graph features like intercepts and function values.

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