Answered

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What is the [tex]$y$[/tex]-intercept of the quadratic function
[tex]\[ f(x) = (x-6)(x-2) \][/tex]

A. \((0, -6)\)
B. \((0, 12)\)
C. \((-8, 0)\)
D. [tex]\((2, 0)\)[/tex]

Sagot :

GinnyAnswer
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]
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