Question

the graph of $f(x)=2x^{2}$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ left 2 units and up 6 units.

Explanation:

Step1: Apply horizontal shift rule

For a function $y = f(x)$, a left - shift of $h$ units gives $y=f(x + h)$. Here, $h = 2$, so $f(x)$ becomes $f(x+2)=2(x + 2)^2$.

Step2: Apply vertical shift rule

For a function $y = f(x)$, a vertical shift of $k$ units up gives $y=f(x)+k$. Here, $k = 6$. So, $g(x)=2(x + 2)^2+6$.

Answer:

$g(x)=2(x + 2)^2+6$