Question 1203271
<br>
The conditions tell us the parabola opens downward, with axis of symmetry at x=-1.<br>
We are given that f(t) is greater than f(0).<br>
By symmetry, f(-2) = f(0) (-2 and 0 are the same distance from the axis of symmetry).<br>
So f(-2) = f(0), f(t) is greater than f(0), the parabola opens downward, and the axis of symmetry is at x=-1.  That means that t must be between -2 and 0, which is condition I.<br>
So I is true.<br>
Given that f(t) is greater than f(0) and f(-2) = f(0), f(t) is also greater than f(-2).  So condition II is false.<br>
We are given that f(t) is greater than f(0). x=1 is farther to the right of the axis of symmetry than x=0; since the parabola opens downward, f(t) is greater than f(1).<br>
So III is true.<br>
I and III are true and II is false, so the answer is (C) I and III only.<br>