Find g(x), where g(x) is the translation 10 units up of f(x)=x2. Write your answer in the form a(x–h)2+k, where a, h, and k are integers. g(x)=

Answer 1

Hi, take a look below for some help!

First, you have f(x) = x² . This is your initial function.

"Translation 10 units up" means what exactly? For every x value on the graph of f(x), we need to move the y value up 10. In other words, all outputs are increased by 10. So if we take the point (2,4) on f(x), the new point would be (2, 4+10) or (2,14) on g(x).

How do we write this out as a function of g(x)?

A translation of 10 units up means that k = 10. Since we are not moving left or right, there is no h value, or h=0. Since no stretches/shrinks are occurring, a = 1 and is unchanged.

Thus,

a=1

h=0

k=10

g(x) = x² + 10

Answer 2

k is the vertical shift. k = 10

Since there's no vertical stretch or shrink a = 1

Since there's no horizontal shift, h = 0

f(x) = x² + 10