Question

The vertex form of a function is g(x) = (x – 3)2 + 9. How does the graph of g(x) compare to the graph of the function

f(x) = x2?

A.g(x) is shifted 3 units left and 9 units up.
B.g(x) is shifted 3 units right and 9 units up.
C.g(x) is shifted 9 units left and 3 units down.
D.g(x) is shifted 9 units right and 3 units down.

Answer 1

the -3 shifts the graph 3 units to the right
and The + 9 moves the graph upwards 9 units

Its B

Answer 2

For this case we have that the main function is given by:

`f (x) = x ^ 2`

First, we apply the horizontal transformation. To do this, we evaluate the function for x-3, that is, we move the graph 3 units to the right.

`f (x-3) = (x-3) ^ 2`

We apply the vertical transformation. To do this, add to the function 9 units, that is, we move the graph 9 units up.

`f (x-3) +9 = (x-3) ^ 2 + 9`

We have then:

`g (x) = (x-3) ^ 2 + 9`

Answer:

B.g (x) is shifted 3 units right and 9 units up.