To find the [tex]\(y\)[/tex]-intercept of the quadratic function [tex]\(f(x) = (x-8)(x+3)\)[/tex], we need to determine the value of the function when [tex]\(x = 0\)[/tex]. The [tex]\(y\)[/tex]-intercept is the point on the graph where the function crosses the [tex]\(y\)[/tex]-axis, which corresponds to [tex]\(x = 0\)[/tex].
Here are the detailed steps to find the [tex]\(y\)[/tex]-intercept:
1. Start with the given quadratic function:
[tex]\[
f(x) = (x-8)(x+3)
\][/tex]
2. Substitute [tex]\(x = 0\)[/tex] into the function:
[tex]\[
f(0) = (0-8)(0+3)
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
f(0) = (-8)(3)
\][/tex]
4. Multiply the two numbers:
[tex]\[
f(0) = -24
\][/tex]
So, the [tex]\(y\)[/tex]-intercept of the function [tex]\(f(x) = (x-8)(x+3)\)[/tex] is at the point where [tex]\(x = 0\)[/tex] and [tex]\(y = -24\)[/tex].
Therefore, the [tex]\(y\)[/tex]-intercept of the quadratic function is [tex]\((0, -24)\)[/tex].
The correct answer is:
[tex]\[
(0, -24)
\][/tex]
