Question

If h(x)=4X^2-16 were shifted 5units to the right and 2 down, what would the new equation be

Answer 1

4(x - 5)^2 - 18.

Explanation:

For a move 5 to the right f(x) ----> f(x - 5).

For a move of 2 down f(x - 5) ----> f(x - 5) - 2.

Answer 2

For this case we have that by definition of function transformation is fulfilled:

Let h> 0:

To graph
`y = f (x-h)`, the graph moves h units to the right.

To graph
`y = f (x + h),` the graph moves h units to the left.

Let k> 0:

To graph
`y = f (x) + k`, the graph k units is moved up.

To graph
`y = f (x) -k`, the graph moves k units down.

So, we have the following function:

`h (x) = 4x ^ 2-16`

5 units on the right:

`h (x) = 4 (x-5) ^ 2-16`

2 units down

`h (x) = 4 (x-5) ^ 2-16-2\\h (x) = 4 (x-5) ^ 2-18`

Answer:

`h (x) = 4 (x-5) ^ 2-18`