Select all of the values of k that shift f(x) = x^2 to the right when f(x) = (x - k)^2. Select the correct answers from the following.

Question

Show all your work.
a) 132
b) 560
c) -130
d) -458
e) -214
f) 210

Answer 1

To shift f(x) = x^2 to the right by k units, we need to replace x in f(x) with (x - k). So the new function is f(x) = (x - k)^2.

To determine the values of k that shift the function to the right, we need to think about what happens when we substitute (x - k) into the original function.

Let's consider a point on the graph of f(x) = x^2, say (1,1). If we want this point to be shifted to (1+k,1) then we need to transform the point so that for the new function, y = f(x) = (x - k)^2, where x = 1+k, y = 1.

Plugging these values in, we get:
1 = (1+k - k)^2
1 = 1

This shows that for the point to be shifted to the right, the values of k should be between -130 and -214.
So the correct answer is:
c) -130
e) -214