Question

the function g is defined as follows g(x)=2x^2 + 2if the graph of g is translated vertically upward by 7 units it becomes the graph of a function h.find the expression for h(x).

Answer 1

$g(x)=2x^2+2$

A vertical translation is given by:

$\begin{gathered} y=f(x)\pm k \\ k\ne0,k\in\R \end{gathered}$

Since g is translated vertically upward by 7 units, then:

$\begin{gathered} h(x)=g(x)+k \\ where\colon \\ g(x)=2x^2+2 \\ k=7 \\ so\colon \\ h(x)=2x^2+2+7 \\ h(x)=2x^2+9 \end{gathered}$