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To solve this problem, we need to find the intercepts of the given equation \( y = -x^2 + 4 \).

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

\[
y = -(0)^2 + 4 = 4
\]

So, the y-intercept is \( (0, 4) \).

### Finding the **x-intercepts**:
The x-intercepts occur when \( y = 0 \). Set the equation equal to zero and solve for \( x \):

\[
0 = -x^2 + 4
\]

\[
x^2 = 4
\]

\[
x = \pm 2
\]

Thus, the x-intercepts are \( (2, 0) \) and \( (-2, 0) \).

### Final Answer:
The intercepts are:
- y-intercept: \( (0, 4) \)
- x-intercepts: \( (-2, 0) \) and \( (2, 0) \)

Therefore, the intercepts are \( (-2, 0), (2, 0), (0, 4) \). 

Would you like a detailed graph or any further explanation?

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Here are 5 related questions to explore further:
1. What is the vertex of the parabola given by the equation \( y = -x^2 + 4 \)?
2. How does the sign of the \( x^2 \) term affect the shape of the parabola?
3. What are the axis of symmetry and the direction of the parabola in this case?
4. How do you find the maximum or minimum value of a quadratic function like this one?
5. How do transformations like shifts and reflections affect the graph of \( y = x^2 \)?

**Tip**: When solving for intercepts, always substitute zero for the other variable (y for x-intercepts, x for y-intercepts).

Find the intercepts and graph the equation by plotting points. y = -x^2 + 4. What are the intercepts?

Learn how to find the x- and y-intercepts for the quadratic equation y = -x^2 + 4. Step-by-step explanation and graphing included. Suitable for students in Grades 8-10.

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