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?

How could the quadratic be written in order to make the minimum value clear ? (hint it will also make the $x$ value where the minimum occurs clear) ... ping me when you have an answer to this. — Donald Splutterwit, Jul 31 '17 at 20:27

score 0 · Accepted Answer · answered Jul 31 '17 at 20:29

0

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

answered Jul 31 '17 at 20:29

Bernard

1 Answers1