Describe how to obtain the graph of g and f if g(x)=2(x + 2)^{2} - 3, h(x)=2x^{2}, and h(x)=2(x - 3)^{2} + 2

Step 1
Properties of the transformation of the graph:
let $y=f(x)=2x^2.$
1) $y=f(x-a)$ shift right by a unit.
2) $y=f(x+a)$ shift left by a unit.
3) $y=f(x)+b$ shift upward by b units.
4) $y=f(x)-b$ shift downward by b units.
5) $y=C\times f(x)$ graph stretched expand vertically if
$C>1$ and compressed vertically if
$C<1.$
Step 2
a) For graph $g(x)=2(x+2{)}^2-3,$
Translate $f(x)=2x^2$ by 2 units left and expand vertically by 2 units then shift it down by 3 units you get
$g(x)=2(x+2{)}^2-3.$
b) For graph $h(x)=2(x-3{)}^2+2$
Translate $f(x)=2x^2$ by 3 units left and expand vertically by 2 units then shift it down by 2 units you get
$h(x)=2(x-3{)}^2+2$
The graph of all functions are shown in below: