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]