Question

The functions f(x) and g(x) are shown in the graph
f(x)=x^2
What is g(x) ?

Answer 1

`g(x)=-x^(2)-4`

Explanation:

we know that

The function g(x) is a vertical parabola open downward with vertex at (0,-4)

The equation of a vertical parabola into vertex form is equal to

`y=a(x-h)^(2)+k`

I assume that g(x) is a reflection of the function f(x) over the line y=-2

so

a=-1 ---> because in the function f(x) the value of a is equal to 1

therefore

`g(x)=-x^(2)-4`