Answer
$f(x)=-3(x+2)^2-5$
See graph
Work Step by Step
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: $(-2,-5),(-3,-8),(-1,-8)$.
