Question

The graphs below have the same shape. What is the equation of the red graph?

Answer 1

g(x)=-x^2 is right for apex

Answer 2

we have

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

the vertex of the function g(x) is the point
`(0,4)`

the vertex of the function f(x) is the point
`(0,0)`

so

the rule of the translation of g(x) to f(x) is

(x,y)------> (x,y-4)

that means

the translation is
`4` units down

therefore

the equation of the function f(x) is

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

therefore

the answer is

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