Let the quadratic be f(x)=ax²+bx+c.
f(0)=0.24, so c=0.24.
f(1)=0.31=a+b+c=a+b+0.24, a+b=0.07.
f(2)=0.36=4a+2b+c=4a+2(0.07-a)+0.24=2a+0.38, 2a=0.36-0.38=-0.02, a=-0.01, so b=0.07+0.01=0.08.
f(x)=-0.01x²+0.08x+0.24.
To express this in the form a(x-h)²+k,
f(x)=0.24-0.01(x²-8x+16-16)=
0.24-0.01(x-4)²+0.16=0.40-0.01(x-4)².
f(x)=-0.01(x-4)² + 0.40.