Which statements describe one of the transformations performed on f (x) = x^2

to create g (x) = 2x^2 + 5?

vertically stretched by a factor of 2 and moved up 5 units

Step-by-step explanation:

f (x) = x^2

f (x+5) means it moved left 5 units.

f (x-5) means it moved right 5 units.

f (x) + 5 means it moved up 5 units.

f (x) - 5 means it moved down 5 units.

One of the transformations we have is that it moved up 5 units.

m (x) = f (x) + 5

m (x) = x^2+5

Now there is another transformation.

f (x) = x^2

a*f (x) means it is either being vertically stretched or compressed. a also tells if we have a reflection (if a is negative) or not (if a is positive).

n (x) = 2x^2 means it has been vertically stretched by a factor of 2.

Let's put it altogether.

g (x) = 2x^2+5

means the parent function has been vertically stretched by a factor of 2 and moved up 5 units