more than 300 years ago,Newton totally solved this kind of quest

F(x)=[(x-2)(x-3)/(1-2)(1-3)]*1/2+[(x-1)(x-3)/(2-1)(2-3)]*1/4+[(x-1)(x-2)/(3-1)(3-2)]*1/4=(1/8)x^2-(5/8)x+1.
We have f(1)=1/2,f(2)=1/4,f(3)=1/4
f(4)=1/2.You check it.
Rguas are smart.I beat almost Aguas in WEIQI(GO),but a smart Rgua beat me.Maybe twenty years ago I would beat him.