Question

For f(x) = x2 and g(x) = (x − 5)2, in which direction and by how many units should f(x) be shifted to obtain g(x)?

Up 5 units
Down 5 units
Left 5 units
Right 5 units

Answer 1

Right 5 units is the answer.

Answer 2

Remark: One of the ways you can do this and be sure of the answer is to graph both equations. Desmos is most helpful. I will do that for you. You can see it below. The key is to look at the vertex. Which way did the low point (vertex) go? Up down, left, right. f(x) is the red parabola. It's vertex is at (0,0) g(x) is the blue parabola. The low point is on the x axis, but where and which way have you gone?