Question

find the x-intercepts of the graph.
y = (x - 8)(x + 8)
x = , x =

Explanation:

Step1: Recall x-intercept definition

To find x-intercepts, set \( y = 0 \) in the equation \( y=(x - 8)(x + 8) \). So we have \( 0=(x - 8)(x + 8) \).

Step2: Apply zero - product property

The zero - product property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \). Here, \( a=(x - 8) \) and \( b=(x + 8) \).

• Case 1: Set \( x - 8=0 \). Solving for \( x \), we add 8 to both sides of the equation: \( x=8 \).
• Case 2: Set \( x + 8=0 \). Solving for \( x \), we subtract 8 from both sides of the equation: \( x=-8 \).

Answer:

\( x=-8 \), \( x = 8 \)