Answer
$f(x)=2(x-4)^2-8=2x^2-16x+24$
Work Step by Step
Step 1. Write a general form of the function $f(x)=a(x-h)^2+k$
Step 2. Use the vertex $(4,-8)$, we have $h=4, k=-8$
Step 3. Use the y-intercept $(0,24)$, we have $a(0-4)^2-8=24$, thus $a=2$
Step 4. Thus the function is $f(x)=2(x-4)^2-8=2x^2-16x+24$
