https://file.aiquickdraw.com/mathbot/file/1729739353127g53mw8ot.jpg

Let's address **Question 4**, which asks for all intercepts (x and y) for the function \( f(x) = x^2 - 4 \).

### **Y-intercept:**
The y-intercept occurs when \( x = 0 \). Substituting into the function:
\[
f(0) = 0^2 - 4 = -4
\]
Thus, the y-intercept is \( (0, -4) \).

### **X-intercepts:**
The x-intercepts occur when \( f(x) = 0 \). So, set the equation equal to zero:
\[
x^2 - 4 = 0
\]
\[
x^2 = 4
\]
\[
x = \pm 2
\]
Thus, the x-intercepts are \( (-2, 0) \) and \( (2, 0) \).

### **Final Answer:**
The intercepts are:
- X-intercepts: \( (-2, 0) \) and \( (2, 0) \)
- Y-intercept: \( (0, -4) \)

So, the correct answer is:  
\[
(0, -4), (-2, 0), (2, 0)
\]

Let me know if you'd like further details! Here are 5 additional questions that build upon this:

1. How do you find intercepts for any general quadratic function?
2. Can a parabola have more than two x-intercepts?
3. What does the vertex of this parabola represent?
4. How would you solve \( f(x) = x^2 - 4 \) using the quadratic formula?
5. What would happen to the intercepts if the equation were \( f(x) = x^2 + 4 \)?

**Tip:** Remember that the x-intercepts of a function occur when the output (y-value) is zero, and the y-intercept occurs when the input (x-value) is zero.

Find all intercepts (x and y) for the function f(x) = x^2 - 4.

Learn how to find the x- and y-intercepts of the quadratic function f(x) = x^2 - 4. This problem covers key algebraic concepts and solving methods. Suitable for students in Grades 7-9.

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