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The equation given in the problem is:

\[
y^2 = x + 16
\]

### Step 1: Finding Intercepts

**X-Intercept:**
- To find the x-intercept, set \( y = 0 \) and solve for \( x \).
  
  \[
  0^2 = x + 16 \quad \Rightarrow \quad x = -16
  \]

  Thus, the x-intercept is \( (-16, 0) \).

**Y-Intercept:**
- To find the y-intercept, set \( x = 0 \) and solve for \( y \).
  
  \[
  y^2 = 0 + 16 \quad \Rightarrow \quad y^2 = 16 \quad \Rightarrow \quad y = \pm 4
  \]

  Therefore, the y-intercepts are \( (0, 4) \) and \( (0, -4) \).

### Step 2: Testing for Symmetry

- **Symmetry with respect to the y-axis:** The equation is already in the form \( y^2 = x + 16 \), which is symmetrical with respect to the y-axis, because if you replace \( y \) with \( -y \), the equation remains the same.

- **Symmetry with respect to the x-axis:** The equation is not symmetrical with respect to the x-axis because replacing \( x \) with \( -x \) doesn't maintain the same form.

- **Symmetry with respect to the origin:** It's not symmetric with respect to the origin because replacing both \( x \) and \( y \) with \( -x \) and \( -y \), respectively, doesn't yield the original equation.

### Conclusion:
- The intercepts are: \( (-16, 0) \), \( (0, 4) \), and \( (0, -4) \).
- The graph is symmetric with respect to the y-axis.

You should choose option A and enter these intercepts: \( (-16, 0), (0, 4), (0, -4) \).

Would you like further details or have any questions?

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Here are 5 related questions:
1. How do you determine symmetry of a graph from its equation?
2. Can a function be symmetric with respect to more than one axis?
3. What is the significance of intercepts in graphing functions?
4. How can you classify conic sections based on equations like \( y^2 = x + 16 \)?
5. How would the graph change if the equation was \( y^2 = x - 16 \)?

**Tip:** Always check for symmetry early when analyzing equations, as it simplifies understanding the graph’s shape.

List the intercepts and test for symmetry. The equation is y^2 = x + 16.

Learn how to find the intercepts and test for symmetry of the equation y^2 = x + 16. This problem covers key algebraic concepts like finding intercepts and identifying symmetry, with a step-by-step explanation suitable for students in Grades 10-12.

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