Question

1. in the $xy$-coordinate system, $(p, 0)$ is one of the points of intersection of the graphs of $y = -x^2+9$ and $y = x^2 - 9$. if $p$ is positive, what is the value of $p$?

a. 3
b. 6
c. 9
d. 18

Explanation:

Step1: Set equations equal (intersection)

Set $-x^2 + 9 = x^2 - 9$

Step2: Rearrange to solve for $x^2$

$9 + 9 = x^2 + x^2$
$18 = 2x^2$

Step3: Solve for $x^2$

$x^2 = \frac{18}{2} = 9$

Step4: Solve for positive $x$

$x = \sqrt{9} = 3$

Answer:

A. 3