Determine the x-intercepts of the following equation.

Question

(−x+1)(−x+2)=y

Answer 1

To find the x-intercepts, we need to set y equal to zero and solve for x.

So, let's set y = 0:

(-x + 1)(-x + 2) = 0

Now, we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero.

So, we have two possibilities:

(-x + 1) = 0 or (-x + 2) = 0

Solving each equation for x:

For -x + 1 = 0:
Adding x to both sides, we get:
1 = x

So, one x-intercept is x = 1.

For -x + 2 = 0:
Adding x to both sides, we get:
2 = x

So, another x-intercept is x = 2.

Therefore, the x-intercepts of the equation are x = 1 and x = 2.