## Precalculus (10th Edition)

We are given the function: $f(x)=\dfrac{1}{2}x^2+x-1$ Rewrite the function building the square: $f(x)=\dfrac{1}{2}(x^2+2x+1)-\dfrac{1}{2}-1=\dfrac{1}{2}(x+1)^2-\dfrac{3}{2}$ 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 $f(x)=\dfrac{1}{2}\left(x+1\right)^2-\dfrac{3}{2}$.