## Precalculus (10th Edition)

$f(x)=-3(x+2)^2-5$ See graph
We are given the function: $f(x)=-3x^2-12x-17$ Complete the square: $f(x)=-3(x^2+4x)-17=-3(x^2+4x+4)+12-17=-3(x+2)^2-5$ We start graphing with the basic function $a(x)=x^2$. We horizontally shift $a(x)$ by 2 units to the left to get $b(x)=(x+2)^2$. Then we vertically stretch $b(x)$ by a factor of 3 to get $c(x)=3(x+2)^2$. Then we reflect $c(x)$ about the $x$-axis to get $d(x)=-3(x+2)^2$. Finally we vertically shift $d(x)$ 5 units downward to get $f(x)=-3(x+2)^2-5$. We use 3 points: $(-2,-5),(-3,-8),(-1,-8)$.