Question

the graph of f(x) shown below has the same shape as the graph of g(x) = x^2, but it is shifted up 1 unit. what is the equation?

Answer 1

The answer is F(x)=x^2+1

Explanation:

Answer 2

`f(x)=x^(2)+1`

Explanation:

we have

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

This is the equation of a vertical parabola open upward

The vertex is a minimum

The vertex is the point (0,0)

The graph of f(x) has the same shape as the graph of g(x), but is shifted up 1 unit

so

The vertex of the function f(x) is (0,1)

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

(x,y) ----> (x,y+1)

therefore

The equation of f(x) is equal to

`f(x)=x^(2)+1`