Finding X-Intercepts of y=(x-5)(x+5): Quadratic Function Analysis

Question

Determine the points of intersection of the function

y=(x5)(x+5) y=(x-5)(x+5)

With the X

Video Solution

Solution Steps

00:00 Find the intersection point with the X-axis
00:03 At the intersection point with the X-axis, the Y value must equal 0
00:07 Substitute Y=0 and solve to find the appropriate X values
00:16 Find what zeros each factor in the product
00:21 This is one solution
00:27 This is the second solution
00:32 And this is the solution to the question

Step-by-Step Solution

In order to find the point of the intersection with the X-axis, we first need to establish that Y=0.

 

0 = (x-5)(x+5)

When we have an equation of this type, we know that one of these parentheses must be equal to 0, so we begin by checking the possible options.

x-5 = 0
x = 5

 

x+5 = 0
x = -5

That is, we have two points of intersection with the x-axis, when we discover their x points, and the y point is already known to us (0, as we placed it):

(5,0)(-5,0)

This is the solution!

Answer

(5,0),(5,0) (5,0),(-5,0)