Question

which point is an ( x )-intercept of the quadratic function ( f(x) = (x - 8)(x + 9) )?
( (0, -8) ) ( (-9, 0) ) ( (0, 8) ) ( (9, 0) )

Explanation:

Step1: Recall x-intercept definition

x-intercepts have \( y = 0 \), so set \( f(x)=0 \).
\( 0=(x - 8)(x + 9) \)

Step2: Solve for x

Use zero - product property: if \( ab = 0 \), then \( a = 0 \) or \( b = 0 \).
Case 1: \( x - 8=0\Rightarrow x = 8 \), so the point is \( (8,0) \) (not in options? Wait, wait, let's check again. Wait, the function is \( f(x)=(x - 8)(x + 9) \). Case 2: \( x+9 = 0\Rightarrow x=-9 \), so the point is \( (-9,0) \).

Answer:

B. \((-9, 0)\) (assuming the options are labeled, and \((-9,0)\) is one of the options as given in the problem)