Over which interval is the graph of f(x) = –x2 3x 8 increasing?

Since you were able to type that negative, I will assume that
f(x)=-x^2+3x+8

the vertex is where the graph changes from increasing to decreasing or vice verca

find theh vertex
-b/2a is x coordinate of vertex where
f(x)=ax^2+bx+c

a=-1
b=3
-3/2(-1)=-3/-2=3/2

we see that the leading coeficient (a) is negative so the graph opens down
it increases then decreases at the vertex

so from negative infinity to 3/2 is interval

in interval nottaion
(⁻∞,3/2]

A=bxh3.2x1.8=5.76 centimeters square