Question

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

Answer 1

Answer:

4(x - 5)^2 - 18.

Step-by-step 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:

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