1. Given that the graph of a quadratic function passes through three points $A\left(\frac{1}{2}, \frac{3}{4}\right) 、 B(-1,3) 、 C(2,3)$, its analytical expression is $\qquad$ .
1. $f(x)=x^{2}-x+1$. Let $f(x)-3=a(x+1)(x-2)$, substituting point $A$ yields $a=1$.