Answer
$\dfrac{5}{4}$
Work Step by Step
As we are given that $a=-1$
and $a =-1 \lt 1$ and this shows a maximum value at the point $h=\dfrac{-b}{2a}=-\dfrac{3}{2(-1)}=\dfrac{3}{2}$
Now, $f(h)=f(\dfrac{3}{2})=-(\dfrac{3}{2})^2+3(\dfrac{3}{2})-1=-\dfrac{9}{4}+\dfrac{9}{2}-1$
or, $f(\dfrac{3}{2})= \dfrac{5}{4}$
