Question

Question 2 of 10 The graphs below have the same shape. What is the equation of the blue graph? f(x) = x2 g(x) = 2 foy 6 -5 g(x) = O A. g(x) = (x - 5)2

Answer 1

Notice that both graphs have the same shape, but the blue curve is the red one after a translation to the right.

In general, given a function h(x), a translation in the x-axis direction is given by the formula

$\begin{gathered} h(x)\to h(x-a) \\ a>0\to\text{ a units to the right} \\ a<0\to\text{ a units to the left} \end{gathered}$

In our case, notice that the vertex of the parabola (0,0) transforms into (5,0)

$\begin{gathered} (0,0)\to)=(5,0)=(5+0,0) \\ \Rightarrow g(x)=f(x-5) \end{gathered}$

Then,

$\Rightarrow g(x)=(x-5)^2$

The answer is g(x)=(x-5)^2