Question

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

Answer 1

Try this, pls:
When any line on graph is moved to the right, for 'x' must be '-'.
When one is moved down, for 'y' must be '-'.
Finaly: y=4(x-5)²-18.
Answer: A.

Answer 2

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

Explanation:

We have been given an equation of a function
`g(x)=4x^2-16`. We are asked to find the formula of the function our g(x) is shifted 5 units to the right and 2 units down.

Let us recall the transformation rules.

`f(x)\rightarrow f(x-a)=\text{Graph shifted to the right by 'a' units}`

`f(x)\rightarrow f(x+a)=\text{Graph shifted to the left by 'a' units}`

`f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by 'a' units}`

`f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by 'a' units}`

Upon shifting our function to the right by 5 units our function would be:

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

Let us shift our given function downwards by 2 units.

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

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

Therefore, option A is the correct choice.