To determine which point is an [tex]$x$[/tex]-intercept of the quadratic function [tex]\( f(x) = (x+6)(x-3) \)[/tex], we need to understand the definition of [tex]$x$[/tex]-intercepts. An [tex]$x$[/tex]-intercept is where the graph of the function crosses the x-axis, which occurs when [tex]\( f(x) = 0 \)[/tex].
Given the function [tex]\( f(x) = (x+6)(x-3) \)[/tex], we set [tex]\( f(x) \)[/tex] to 0 and solve for [tex]\( x \)[/tex]:
[tex]\[
(x + 6)(x - 3) = 0
\][/tex]
This equation will be true when any of its factors is equal to zero.
1. Solve for [tex]\( x + 6 = 0 \)[/tex]:
[tex]\[
x + 6 = 0
\][/tex]
[tex]\[
x = -6
\][/tex]
2. Solve for [tex]\( x - 3 = 0 \)[/tex]:
[tex]\[
x - 3 = 0
\][/tex]
[tex]\[
x = 3
\][/tex]
Therefore, the [tex]$x$[/tex]-intercepts of the function [tex]\( f(x) = (x+6)(x-3) \)[/tex] are at [tex]\( x = -6 \)[/tex] and [tex]\( x = 3 \)[/tex].
So, the points where the function crosses the x-axis are [tex]\( (-6, 0) \)[/tex] and [tex]\( (3, 0) \)[/tex].
Looking at the given choices, the correct answer for which point is an [tex]$x$[/tex]-intercept of the quadratic function [tex]\( f(x) = (x+6)(x-3) \)[/tex] is:
[tex]\[
\boxed{(-6,0)}
\][/tex]
