Answer
$f(x)=-2(x+3)^2+5$
See graph
Work Step by Step
We are given the function:
$f(x)=-2x^2-12x-13$
Complete the square:
$f(x)=-2(x^2+6x)-13=-2(x^2+6x+9)+18-13=-2(x+3)^2+5$
We start graphing with the basic function $a(x)=x^2$.
We horizontally shift $a(x)$ by 3 units to the left to get $b(x)=(x+3)^2$.
Then we vertically stretch $b(x)$ by a factor of 2 to get $c(x)=2(x+3)^2$.
Then we reflect $c(x)$ about the $x$-axis to get $d(x)=-2(x+3)^2$.
Finally we vertically shift $d(x)$ 5 units upward to get $f(x)=-2(x+3)^2+5$.
We use 3 points: $(-4,3),(-3,5),(-2,3)$.
