Question

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

Answer 1

Answer:

C

Step-by-step 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

Answer:

The graph that shows the same shape is:

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

Step-by-step 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:

$g(x)=-3\neq 3$

Hence, option: A is incorrect.

B)

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

when x=0 we have:

$g(x)=(3)^2=9\neq 3$

Hence, option: B is incorrect.

D)

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

when x=0 we have:

$g(x)=(-3)^2=9\neq 3$

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.