Answer
$f(x)=-2(x+3)^2+5$
Work Step by Step
Completing the square:
$f(x)=-2x^2-12x-13$
$f(x)=-2(x^2+6x)-13$
$f(x)=-2(x^2+6x+(\frac{6}{2})^2)+2\cdot(\frac{6}{2})^2-13$
$f(x)=-2(x^2+6x+3^2)+2\cdot3^2-13$
$f(x)=-2(x+3)^2+2\cdot9-13$
$f(x)=-2(x+3)^2+18-13$
$f(x)=-2(x+3)^2+5$
Graphing the function:
1st step (black graph): The parent function: $y=x^2$
2nd step (green graph): Reflect over the x-axis. $y=-x^2$
3rd step (orange graph): Stretch by a factor of 2. $y=-2x^2$
4th step (red graph): Shift 5 units up. $y=-2x^2+5$
Final step (blue graph): Shift left by 3 units. $y=-2(x+3)^2+5$
