Answer
$y= -3x^2+12x-16$
Work Step by Step
Step 1. With a vertex at $(2,-4)$, we can write the equation as $y=a(x-2)^2-4$ where $a$ is unknown.
Step 2. For the y-intercept $-16$, let $x=0$, we have $-16=a(0-2)^2-4$, thus $a=-3$
Step 3. The equation is $y=-3(x-2)^2-4=-3x^2+12x-16$
