Question

what are the x-intercepts of the following quadratic function?
y = (x - 12)(x - 48)
select all correct options:
(12, 0)
(-48, 0)
(48, 0)
(-12, 0)

Explanation:

Step1: Recall x - intercept definition

To find the x - intercepts of a function \(y = f(x)\), we set \(y=0\) and solve for \(x\). So for the function \(y=(x - 12)(x - 48)\), we set \(y = 0\).
\[0=(x - 12)(x - 48)\]

Step2: Apply zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). So we have two cases:
Case 1: \(x-12=0\)
Solving for \(x\), we add 12 to both sides of the equation: \(x=12\). So one x - intercept is \((12,0)\) (since when \(x = 12\), \(y = 0\)).
Case 2: \(x - 48=0\)
Solving for \(x\), we add 48 to both sides of the equation: \(x = 48\). So the other x - intercept is \((48,0)\) (since when \(x=48\), \(y = 0\)).

Answer:

A. (12, 0), C. (48, 0)