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Let's analyze the equation \(x^2 + y - 16 = 0\) step by step.

### 1. **Finding the Intercepts**
   - **X-intercepts**: Set \(y = 0\) in the equation to find the x-intercepts.
     \[
     x^2 + 0 - 16 = 0 \quad \Rightarrow \quad x^2 = 16 \quad \Rightarrow \quad x = \pm 4
     \]
     So the x-intercepts are \((4, 0)\) and \((-4, 0)\).

   - **Y-intercept**: Set \(x = 0\) in the equation to find the y-intercept.
     \[
     0^2 + y - 16 = 0 \quad \Rightarrow \quad y = 16
     \]
     So the y-intercept is \((0, 16)\).

   Therefore, the intercepts are:
   \[
   (4, 0), (-4, 0), (0, 16)
   \]

### 2. **Testing for Symmetry**
   - **Symmetry with respect to the x-axis**: Replace \(y\) with \(-y\) in the equation and check if the equation remains unchanged.
     \[
     x^2 - y - 16 = 0
     \]
     This is not the same as the original equation, so **the graph is not symmetric with respect to the x-axis**.

   - **Symmetry with respect to the y-axis**: Replace \(x\) with \(-x\) and check if the equation remains unchanged.
     \[
     (-x)^2 + y - 16 = 0 \quad \Rightarrow \quad x^2 + y - 16 = 0
     \]
     This is the same as the original equation, so **the graph is symmetric with respect to the y-axis**.

   - **Symmetry with respect to the origin**: Replace both \(x\) with \(-x\) and \(y\) with \(-y\).
     \[
     (-x)^2 - y - 16 = 0 \quad \Rightarrow \quad x^2 - y - 16 = 0
     \]
     This is not the same as the original equation, so **the graph is not symmetric with respect to the origin**.

### Answers to Questions:
1. Intercepts: **A. (4, 0), (-4, 0), (0, 16)** (option A).
2. Symmetry with respect to the x-axis: **No**.
3. Symmetry with respect to the y-axis: **Yes**.
4. Symmetry with respect to the origin: **No**.

---

Would you like more details or have any questions?  
Here are 5 related questions to expand your understanding:

1. How do you determine the number of intercepts an equation has?
2. What other types of symmetry can a graph exhibit?
3. Can an equation be symmetric with respect to both axes and the origin at the same time?
4. How do higher-degree polynomials behave with respect to intercepts and symmetry?
5. What are the key differences between even and odd functions in terms of symmetry?

**Tip:** For polynomial equations, even powers of variables typically suggest symmetry with respect to the y-axis!

For the given equation, list the intercepts and test for symmetry. The equation is x^2 + y - 16 = 0. What are the intercepts? Is the graph symmetric with respect to the x-axis, y-axis, and origin?

Learn how to find the intercepts and test for symmetry for the equation x^2 + y - 16 = 0. This problem covers intercept calculations and symmetry tests, focusing on the x-axis, y-axis, and origin.

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