To find the [tex]$y$[/tex]-intercept of the quadratic function [tex]\( f(x) = (x-6)(x-2) \)[/tex], we need to determine the value of the function when [tex]\( x = 0 \)[/tex]. The [tex]$y$[/tex]-intercept occurs where the graph of the function crosses the [tex]$y$[/tex]-axis, which is at [tex]\( x = 0 \)[/tex].
Let's follow these steps to find the [tex]$y$[/tex]-intercept:
1. Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(0) = (0 - 6)(0 - 2)
\][/tex]
2. Simplify the expression by performing the operations inside the parentheses:
[tex]\[
f(0) = (-6)(-2)
\][/tex]
3. Multiply the results:
[tex]\[
f(0) = 12
\][/tex]
Thus, the [tex]$y$[/tex]-intercept of the function is [tex]\( (0, 12) \)[/tex].
Therefore, the correct answer is:
[tex]\[
(0, 12)
\][/tex]
