The equation provided is:

$y = x^2 - 16$

Finding the Intercepts:

1. Y-Intercept: The y-intercept is found by setting $x = 0$ and solving for $y$.

   $y = 0^2 - 16 = -16$

   So, the y-intercept is the point $(0, -16)$.

2. X-Intercepts: The x-intercepts are found by setting $y = 0$ and solving for $x$.

   $0 = x^2 - 16$ $x^2 = 16$ $x = \pm 4$

   Therefore, the x-intercepts are at $(4, 0)$ and $(-4, 0)$.

Answer:

• The intercepts are: $(-4, 0), (4, 0), (0, -16)$.
• For the multiple choice, you would select A, and type these intercepts as ordered pairs.

Graphing:

This equation represents a parabola that opens upwards with its vertex at $(0, -16)$ and intercepts at $(-4, 0)$, $(4, 0)$, and $(0, -16)$.

Would you like more details or have any further questions?

Here are 5 related questions to explore this further:

1. What is the vertex of the parabola?
2. How does the value of the constant term affect the position of the graph?
3. What would happen if the equation was $y = -x^2 - 16$?
4. How would you find the axis of symmetry for this parabola?
5. Can you describe how to complete the square for the equation $y = x^2 - 16$?

Tip: Always start by finding intercepts to graph parabolas effectively, as they provide key points to structure your graph.