Question

PLEASE ANSWER!!
The graph below have the same shape. what is the equation for the red graph?

Answer 1

C

Explanation:

given a function f(x) then

f(x) + c ← denotes a vertical translation of f(x)

• If c > 0 then shift vertically up

• If c < 0 then shift vertically down

Here the vertex of f(x) is at the origin and the vertex of g(x) is (0, 3 ), that is 3 units vertically up

Hence g(x) = x² + 3 → C

Answer 2

The graph that shows the same shape is:

C.
`g(x)=x^2+3`

Explanation:

We are given the parent function f(x) as:

`f(x)=x^2`

Now, after looking at the graph we see that the graph is a translation of a function f(x) 3 units upward.

since, the vertex of graph is at (0,3).

Now, we will check which graph passes through the point (0,3)

A)

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

at x=0 we have:

`g(x)=-3\\eq 3`

Hence, option: A is incorrect.

B)

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

when x=0 we have:

`g(x)=(3)^2=9\\eq 3`

Hence, option: B is incorrect.

D)

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

when x=0 we have:

`g(x)=(-3)^2=9\\eq 3`

Hence, option: D is incorrect.

Hence, we are left with option: C

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

It passes through (0,3).

Also, we know that the translation g(x) of a parent function f(x) k units upward is given by:

`g(x)=f(x)+k`

Here k=3

Hence,

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

Option: C is correct.