Question

HELP PLEASE!

if g(x)= 4x^2-16 were shifted 9 units to the right and 1 down, what would be the new equation?

A. h(x) = 4(x+9)^2 - 17
B. h(x) = 4(x-17)^2 -9
C. h(x) = 4(x-9)^2 - 17
D. h(x) = 4(x-7)^2 + 16

Answer 1

C.
`h(x)=4(x-9)^2-17`

Explanation:

We have been given a function
`g(x)=4x^2-16`. We re asked to find the equation for function that is obtained from shifting our given function 9 units to the right and 1 down.

Let us recall transformation rules.

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

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

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

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

Let us shift our given function to right by 9 units as:

`g(x)=4(x-9)^2-16`

Now, we will shift our function downwards by 1 unit.

`g(x)=4(x-9)^2-16-1`

`g(x)=4(x-9)^2-17`

Therefore, our required function would be
`h(x)=4(x-9)^2-17` and option C is the correct choice.

Answer 2

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units left

f(x - n) - shift the graph n units right

-----------------------------------------------------------------

g(x) = 4x² - 16

Shift 9 units right and 1 unit down. Therfore:

g(x - 9) - 1 = 4(x - 9)² - 16 - 1 = 4(x - 9)² - 17

Answer: A. h(x) = 4(x - 9)² - 17