Question

3. Select the correct transformations: y=(x-4)^2+12 pointsThe vertex translates 1 unit to the right and 4 units to the leftThe vertex translates 4 units to the right and 1 unit upwardThe vertex translates 1 unit to the right and 4 units downwardsThe vertex translates 4 units to the left 4 and 1 unit upward

Answer 1

The vertex translates 4 units to the right and 1 unit upward

Explanation:

Suppose we have a function f(x).

To translate the function a units to the left, we need to find f(x + a).

To translate the function a units to the right, we need to find f(x - a).

To translate the function a units upward, we need to find f(x) + a

To translate the function a units downwards, we need to find f(x) - a.

In this question.

We start with:

f(x) = x²

First, we look at changes in x. We have

f(x-4) = (x - 4)². So a translation of 4 units to the right.

Then

f(x - 4) + 1 = (x-4)² + 1

One unit upwards.

The correct answer is:

The vertex translates 4 units to the right and 1 unit upward