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

A) g(x) = (x-4)^2
B) g(x) = (x+4)^2
C) g(x) = x^2 + 4
D) g(x) = x^2 - 4

Question

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MrRoyal MrRoyal · Answer 1 · 2021-12-07T09:56:00+01:00

The graphs of f(x) and g(x) are related by transforming one of the two graphs.

The equation of the blue graph is [tex]\mathbf{g(x) =(x - 4)^2}[/tex]

From the graphs, we have:

[tex]\mathbf{f(x) =x^2}[/tex]

f(x) is transformed to the right by 4 units.

The rule of this transformation is:

[tex]\mathbf{g(x) \to f(x - 4)}[/tex]

So, we start by calculating f(x - 4)

Given that:

[tex]\mathbf{f(x) =x^2}[/tex]

Substitute x - 4 for x in f(x)

[tex]\mathbf{f(x - 4) =(x - 4)^2}[/tex]

Also, recall that:

[tex]\mathbf{g(x) \to f(x - 4)}[/tex]

So, we have:

[tex]\mathbf{g(x) =(x - 4)^2}[/tex]

Hence, the equation of g(x) is [tex]\mathbf{g(x) =(x - 4)^2}[/tex]