Question

Determine the x-intercepts of the following equation.
left parenthesis, x, minus, 4, right parenthesis, left parenthesis, x, minus, 3, right parenthesis, equals, y
(x−4)(x−3)=
y
Answer
Attempt 1 out of 2
Multiple Choice Answers
left parenthesis, 12, comma, 0, right parenthesis(12,0)
left parenthesis, 0, comma, 12, right parenthesis(0,12)
left parenthesis, 4, comma, 0, right parenthesis, and , left parenthesis, minus, 3, comma, 0, right parenthesis(4,0) and (−3,0)
left parenthesis, 0, comma, 4, right parenthesis, and , left parenthesis, 0, comma, 3, right parenthesis(0,4) and (0,3)
left parenthesis, 4, comma, 0, right parenthesis, and , left parenthesis, 3, comma, 0, right parenthesis(4,0) and (3,0)
left parenthesis, 0, comma, minus, 12, right parenthesis(0,−12)

Answer 1

To find the x-intercepts of the equation \((x - 4)(x - 3) = y\), we set \(y = 0\):

\[
(x - 4)(x - 3) = 0
\]

Now, we solve for \(x\) by setting each factor equal to zero:

1. \(x - 4 = 0\)
- Solving this gives \(x = 4\).

2. \(x - 3 = 0\)
- Solving this gives \(x = 3\).

Thus, the x-intercepts are the points where \(y = 0\):
- \((4, 0)\)
- \((3, 0)\)

From the given multiple-choice answers, the correct option is:

\[
\left(4, 0\right) \text{ and } \left(3, 0\right)
\]

So, the answer is: **\((4, 0)\) and \((3, 0)\)**.