Simple Quadratic function

Question

If we say that the minimum of a quadratic function is -3

And the sum of its zeros/roots is 2

And I want to find the value of F(1)

How do I write down the given here in a more applicable form to the question?

Answer 1

The extremum of a quadratic function happens at the half-sum of its roots (whether real of complex), thus at $x=1$, so $F(1)=-3$.

Note this function is equal to $$F(x)=a(x-1)^2-3 \quad\text{for some} \,a\in\mathbf R.$$