If -5 is added to a number and the sum is doubled, the result is 9 less than the number

The equation is 2(-2+x)=y and result is 9 less than the number

So the answer is 2(-2+x)=y-9

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2