Answer
$y=2x^2-8x+11$
Work Step by Step
1. Start from the standard form $y=a(x-h)^2+k$
2. As the apex $(2,3)$ is given, we have $h=2, k=3$ and the equation becomes $y=a(x-2)^2+3$
3. As point $(1,5)$ is on the curve, we have $5=a(1-2)^2+3$ which gives $a=2$
4. Thus the equation is $y=2(x-2)^2+3=2x^2-8x+11$
Note: you can also set up a system of equations to solve $a,b,c$, but this is not required by the exercise.
