Question

The graph of F(x), shown below, has the same shape as the graph of G(x) = x2, but it is shifted up 3 units. What is its equation?

Answer 1

For this case, the parent function is given by:

`G (x) = x ^ 2`
Applying the following transformation we have:
Vertical displacement
Assume k> 0,
To graph y = f (x) + k, move the graph k units up.
We have then:

`F (x) = G (x) + 3 F (x) = x ^ 2 + 3`
Answer:
the equation of F (x) is given by:

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