Question

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

Answer 1

Option C.
`g(x)=(x+5)^(2)`

Explanation:

we know that

The equation of the parent function f(x) (red graph) is

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

This is a vertical parabola open upward

The vertex is the point (0,0) (the origin)

The function g(x) (blue graph) is a vertical parabola open upward

The vertex is the point (-5,0)

The transformation of f(x) to g(x) has the following rule

f(x) -----> g(x)

(0,0) ----> (-5,0)

(x,y) ----> (x-5,y)

That means----> The transformation is a translation of 5 units at left

therefore

The equation of g(x) is

`g(x)=(x+5)^(2)`