Answer
See graphs
Work Step by Step
We are given the function:
$f(x)=\dfrac{2}{3}x^2+\dfrac{4}{3}x-1$
Rewrite the function building the square:
$f(x)=\dfrac{2}{3}(x^2+2x+1)-\dfrac{2}{3}-1=\dfrac{2}{3}(x+1)^2-\dfrac{5}{3}$
We start graphing the parent function $a(x)=x^2$.
Then horizontally shift $a(x)$ one unit to the left to get $b(x)=\left(x+1\right)^2$.
Then vertically compress $b(x)$ by a factor of $\dfrac{1}{2}$ to get $c(x)=\dfrac{1}{2}\left(x+1\right)^2$.
Finally vertically shift $c(x)$ $\dfrac{3}{2}$ units downward to get $f(x)=\dfrac{1}{2}\left(x+1\right)^2-\dfrac{3}{2}$.
