List the​ intercept(s) of the following equation.
yequalsx squared minus 16

The given equation is:

\[
y = x^2 - 16
\]

To find the **intercepts**, we look for the points where the graph crosses the axes. This includes both **x-intercepts** and the **y-intercept**.

### 1. **Y-intercept**:
The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation:

\[
y = (0)^2 - 16 = -16
\]

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

### 2. **X-intercepts**:
The x-intercepts occur when \( y = 0 \). Setting the equation equal to zero:

\[
0 = x^2 - 16
\]

This can be factored as:

\[
0 = (x - 4)(x + 4)
\]

So, \( x = 4 \) and \( x = -4 \).

Thus, the x-intercepts are \( (4, 0) \) and \( (-4, 0) \).

### Summary:
- **Y-intercept**: \( (0, -16) \)
- **X-intercepts**: \( (4, 0) \) and \( (-4, 0) \)

Would you like further details or have any questions?

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Here are five related questions:
1. How do you find intercepts for different types of functions, like cubic functions?
2. What does the graph of \( y = x^2 - 16 \) look like, and how are the intercepts related to its shape?
3. How can we determine if a quadratic equation will have real x-intercepts or not?
4. Can a quadratic function have no x-intercepts? Why?
5. How do we find the vertex of a parabola like \( y = x^2 - 16 \)?

**Tip**: When solving quadratic equations, always check if the equation can be factored before using other methods like the quadratic formula!

List the intercept(s) of the following equation. y = x^2 - 16

Learn how to find the x-intercepts and y-intercept of the quadratic equation y = x^2 - 16. This solution explores factoring quadratic equations and applying the zero product property. Suitable for students in Grades 8-10.

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