Question

The graph of F(x), shown below in pink, has the same shape as the graph of G(x) = x2, but it is flipped over the x-axis and shifted down 2 units. What is its equation?

Answer 1

We are given

graph of f(x) is same as g(x)

so,

`f(x)=g(x)=x^2`

Firstly, it is flipped over x-axis

It means that it is reflected about x-axis

so, we can multiply y-value by -1

and we get

`f(x)=-x^2`

now, it is shifted down by 2 units

So, we can subtract y-value by 2

and we get

`f(x)=-x^2-2`

so, our new equation is

`f(x)=-x^2-2`................Answer