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:
 $F (x) = x ^ 2 + 3$