Question

what is the y-intercept of the quadratic function f(x) = (x - 8)(x + 3)? (8,0) (0,3) (0,-24) (-5,0)

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \(y = f(x)\) is the point where \(x = 0\). So we need to find \(f(0)\) for the function \(f(x)=(x - 8)(x + 3)\).

Step2: Substitute \(x = 0\) into the function

Substitute \(x = 0\) into \(f(x)=(x - 8)(x + 3)\):
\(f(0)=(0 - 8)(0 + 3)\)
First, calculate the values inside the parentheses: \(0-8=-8\) and \(0 + 3=3\).
Then multiply these two results: \((-8)\times(3)=-24\).
So when \(x = 0\), \(y=-24\), and the y - intercept is \((0,-24)\).

Answer:

(0, -24)