Question

The graph of the function h(x) = 2x2 is shown on the grid below. Graph the function g(x) = 2(x + 1)2 – 8 in the interactive graph.

Answer 1

inConsider the h(x) as the parental function

$h(x)=2x^2$

To determine the function g(x), there were two transformations performed to the parental function.

-First, they added 1 to the x-term, which results on a horizontal translation of one unit to the left

$h(x+1)=2(x+1)^2$

-Second, there were subtracted 8 units to the function, which results in a vertical translation down:

$\begin{gathered} g(x)=h(x+1)-8 \\ g(x)=2(x+1)^2-8 \end{gathered}$

So the function g(x) has the same shape as function h(x) but its vertex is on the coordinates (-1,-8)