Solve y = -4x² + 9: Finding X-Axis Intersection Points

Determine the points of intersection of the function

$9-y=4x^2$

With the X

To solve this problem, we'll follow these steps:

• Step 1: Set $y = 0$ in the given equation $9 - y = 4x^2$ to get the simplified equation $9 = 4x^2$.
• Step 2: Rearrange the equation to isolate $x^2$, yielding $4x^2 = 9$.
• Step 3: Solve for $x^2$ by dividing each side by 4, resulting in $x^2 = \frac{9}{4}$.
• Step 4: Take the square root of both sides to find $x = \pm \frac{3}{2}$.

Therefore, the points of intersection with the x-axis are $(-\frac{3}{2}, 0)$ and $(\frac{3}{2}, 0)$.

Referring to the provided choices, this correctly corresponds to choice 3.