Find X-Intercepts: Solving y = 16 - x² When y Equals Zero

Determine the points of intersection of the function

$y=16-x^2$

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

00:06 Substitute Y=0 in our equation and solve for the intersection point

00:13 Isolate X

00:21 Extract the root

00:26 Remember when extracting a root there are 2 solutions (positive and negative)

00:31 These are the X values

00:35 Y = 0 as we substituted at the beginning

00:46 And this is the solution to the question

Step-by-Step Solution

To determine the points of intersection of the function $y = 16 - x^2$ with the x-axis, we follow these steps:

Step 1: Set the equation equal to zero since the x-axis corresponds to $y = 0$ .
$y = 16 - x^2 = 0$
Step 2: Rearrange the equation to isolate $x^2$ .
Adding $x^2$ to both sides gives: $x^2 = 16$ .
Step 3: Solve the equation $x^2 = 16$ for $x$ by taking the square root of both sides.
$x = \pm \sqrt{16}$ results in $x = \pm 4$ .
Step 4: Determine the intersection points. For $x = 4$ , the point of intersection is $(4, 0)$ , and for $x = -4$ , the point of intersection is $(-4, 0)$ .

Therefore, the points of intersection of the parabola with the x-axis are $(-4,0)$ and $(4,0)$ .

This corresponds to the answer choice: $(-4,0),(4,0)$ .