Question

The graphs below have the same shape. What is the equation of the blue graph

Answer 1

Option: C is the correct answer.

The equation of the Blue graph is:

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

Explanation:

We are given a graph of a parent function F(x) as:

`F(x)=x^2`

We know that the function G(x) is nothing but a translation transformation of the parent function by some units to the left.

Also we know that the transformation k units to the left or right is denoted by:

F(x) → F(x+k)

if k>0 then the shift is k units to the left.

and if k<0 then the shift is k units to the right.

Here we have k= 3 and shift is to the left.

Hence, the equation of translated function is:

G(x)=F(x+3)

i.e.
`G(x)=(x+3)^2`