Answer
See graphs
Work Step by Step
We are given the function:
$f(x)=-2x^2+6x+2$
Rewrite the function building the square:
$f(x)=-2\left(x^2-3x+\dfrac{9}{4}\right)+\dfrac{9}{2}+2=-2\left(x-\dfrac{3}{2}\right)^2+\dfrac{13}{2}$
We start graphing the parent function $a(x)=x^2$.
Then horizontally shift $a(x)$ $\dfrac{3}{2}$ units to the right to get $b(x)=\left(x-\dfrac{3}{2}\right)^2$.
Then vertically stretch $b(x)$ by a factor of 2 to get $c(x)=2\left(x-\dfrac{3}{2}\right)^2$.
Then reflect $c(x)$ across the $x$_axis to get $d(x)=-2\left(x-\dfrac{3}{2}\right)^2$.
Finally vertically shift $d(x)$ $\dfrac{13}{2}$ units upward to get $f(x)=-2\left(x-\dfrac{3}{2}\right)^2+\dfrac{13}{2}$.
