Find g(x), where g(x) is the translation 3 units left 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:

The answer should be in the form of a(x-h)² + k.

Since we are not translating up or down, the k value is 0. We will not be adding any values to the outputs of the original equation here. a will equal 1 since no stretches are occurring. So we are left with the h value.

f(x) = x² is given.

g(x) = a horizontal translation of 3 units left. This means that the h value is -3, because in order to move left, you need to take 3 away from all x values (inputs). So the point (2,4) on f(x) would become (-1,4) on g(x).

How do we write this?

g(x) = f(x-h) where h = -3.

So this is g(x) = f(x - (-3)) = f(x+3)

g(x) = (x+3)²

Answer 2

h is the translation of the graph to the right, and k is the translation of the graph up. We keep the a term from the original function, which in this case is 1. Therefore, since the graph is translated 3 units left, we have:

g(x) = (x + 3)²