To determine the [tex]$x$[/tex]-intercepts of the quadratic function [tex]\( f(x) = (x+6)(x-3) \)[/tex], you need to find the values of [tex]\( x \)[/tex] where the function equals zero. This is achieved by setting [tex]\( f(x) = 0 \)[/tex] and solving for [tex]\( x \)[/tex].
1. Start with the given function:
[tex]\[
f(x) = (x+6)(x-3)
\][/tex]
2. Set the function equal to zero to find the [tex]$x$[/tex]-intercepts:
[tex]\[
(x+6)(x-3) = 0
\][/tex]
3. Use the Zero Product Property, which states that if a product of factors is zero, at least one of the factors must be zero. Therefore, set each factor equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[
x + 6 = 0 \quad \text{or} \quad x - 3 = 0
\][/tex]
4. Solve each equation separately:
[tex]\[
x + 6 = 0 \quad \Rightarrow \quad x = -6
\][/tex]
[tex]\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\][/tex]
So, the [tex]$x$[/tex]-intercepts of the function are:
[tex]\[
(-6, 0) \quad \text{and} \quad (3, 0)
\][/tex]
Among the given choices, the point [tex]\((-6, 0)\)[/tex] is listed. Therefore, the [tex]$x$[/tex]-intercept of the quadratic function [tex]\( f(x) = (x+6)(x-3) \)[/tex] that matches one of the given options is:
[tex]\[
(-6, 0)
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{(-6, 0)}
\][/tex]
