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

Answer:

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

Step-by-step 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.