Answer
$-2(x+3)^2+5$
See graph.
Work Step by Step
Step 1. $f(x)=-2x^2-12x-13=-2(x^2+6x+9)+18-13=-2(x+3)^2+5$
Step 2. To graph $f(x)$, start with $y=x^2$, shift $3$ unit to the left, stretch vertically by a factor of 2, reflect across the x-axis, then shift $5$ units up. See graph.