To find the \( y \)-intercept of a quadratic function, you need to determine the value of the function when \( x = 0 \). The \( y \)-intercept is the point where the graph of the function crosses the \( y \)-axis.
Given the quadratic function:
[tex]\[ f(x) = (x - 6)(x - 2) \][/tex]
Let's substitute \( x = 0 \) into the function to find the \( y \)-intercept:
[tex]\[ f(0) = (0 - 6)(0 - 2) \][/tex]
First, simplify the expressions inside the parentheses:
[tex]\[ f(0) = (-6)(-2) \][/tex]
Next, multiply the two numbers:
[tex]\[ f(0) = 12 \][/tex]
Therefore, the \( y \)-intercept occurs at the point \( (0, 12) \).
So, the correct answer is:
[tex]\[ (0, 12) \][/tex]
