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

Determine the points of intersection of the function

$9-y=4x^2$

With the X

Video Solution

Solution Steps

00:00 Find the intersection point of the function with the X-axis

00:03 At the intersection point with the X-axis, Y equals 0

00:07 Substitute Y=0 in our equation and solve to find the intersection point

00:18 Isolate X

00:26 Extract the root

00:35 Remember when extracting a root there are 2 solutions (positive and negative)

00:38 Calculate root 9 and root 4

00:48 And this is the solution to the question

Step-by-Step Solution

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.