Answer
$t=-\frac{b}{2a}$
Work Step by Step
This situation is represented by the vertex of the parabola:
Vertex: $(-\frac{b}{2a},f(-\frac{b}{2a}))$
So, $t=-\frac{b}{2a}$ and $P(t)=f(-\frac{b}{2a}))$
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