Find g(x), where g(x) is the translation 6 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

k is the vertical shift so k = 6

no stretch or shirnk so a = 1

no horizontal shift so h = 0

f(x) = x² + 6

Answer 2

g(x) is a function that is a 6 up translation of f(x) = x²

First I want to write f(x) in the form requested to illustrate the concept

f(x) = 1(x - 0)² + 0

Notice how simply writing the a=1, h=0, and k=0 values don't change the f(x) into a different function. We could simplify it back to f(x) = x².

Vertical translations are controlled by the k value. We need to add 6 to the k value of f(x) to get the correct k value for g(x). 0 + 6 = 6. Thus, the correct k value for g(x) is 6.

g(x) = 1(x - 0)² + 6

Answer 3

k is the variable that corresponds with a vertical translation.

g(x)=x²+6