Question

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

graph?
F(X) = x2
5
G(X) = ?
5
G(X) =

Answer 1

`g(x) = (x - 2)^2 + 1`

Explanation:

Given

`f(x) = x^2`

Required

Determine g(x)

f(x) represents the parent function. And from the graph, we have:

`f(x) = x^2`

f(x) is first shifted 2 units right.

The rule is:

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

So, we have:

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

Next, f'(x) is shifted 1 unit up to give g(x), the blue graph.

The rule to this is:

`g(x) = f'(x) + 1`

`g(x) = (x - 2)^2 + 1`