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For which pair of functions is the vertex of g(x) 3 units to the right of the vertex of f(x)?

For which pair of functions is the vertex of g(x) 3 units to the right of the vertex-example-1
User XMozart
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1 Answer

3 votes

Answer: A.


f(x)=x^2\text{ and }g(x)=(x-3)^2

Step-by-step explanation

Given:


f(x)=x^2

As we want to move the vertex 3 units to the right, this means we have to make a transformation on x (not y). Then, we have to make x = 3 when y = 0, meaning:


\begin{gathered} x=3 \\ x-3=0 \end{gathered}

Thus:


g(x)=(x-3)^2

We have to subtract 3 inside the parenthesis because if we add/subtract 3 outside, it would have an impact on y.

User Sepehr Sobhani
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