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To determine where the equation \( y = -x^2 + 4 \) crosses the x-axis, we need to find the points where \( y = 0 \). In other words, we solve for \( x \) when \( y = 0 \):

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

Rearranging the equation to isolate \( x^2 \):

\[
x^2 = 4
\]

Now, solve for \( x \) by taking the square root of both sides:

\[
x = \pm 2
\]

Thus, the equation crosses the x-axis at the points \( x = 2 \) and \( x = -2 \). Therefore, the x-intercepts are at \( (2, 0) \) and \( (-2, 0) \).

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Here are five related questions to expand on this topic:
1. How do you find the vertex of the parabola represented by \( y = -x^2 + 4 \)?
2. What is the significance of the coefficient of \( x^2 \) in a quadratic equation?
3. How can you determine whether the parabola opens upwards or downwards?
4. What is the domain and range of the function \( y = -x^2 + 4 \)?
5. How do you find the axis of symmetry for a parabola?

**Tip:** For quadratic equations of the form \( y = ax^2 + bx + c \), the x-axis crossings (x-intercepts) can be found using the quadratic formula if needed!

Where does the equation y = -x^2 + 4 cross the x-axis?

Learn how to find the points where the quadratic equation y = -x^2 + 4 crosses the x-axis. This involves solving for x when y = 0, applying key concepts from quadratic equations and parabolas. Suitable for students in Grades 8-10.

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