Watch this video to learn about quadratic functions.

https://www.youtube.com/watch?v=QJU-nfaTSto

y = -x^2-3x

compare to y = ax^2+bx+c

a=-1, b=-3, c=0

It opens downward because a is negative.

The greatest value is found at the vertex.

the x-coordinate of the vertex is -b/(2a)

-(-3)/(2*-1) = -3/2

Find the y-coordinate on the vertex by substituting

y = -x^2-3x
y = -(-3/2)^2-3(-3/2)
y = -9/4+9/2
y = -9/4+18/4
y = 9/4

So the vertex is the point (-3/2, 9/4).

And the y-value of the vertex is the greatest value of
the function if the graph opens downward, and the least
value if the graph opens upward.

So the greatest value is 9/4 or 2.25.

Here's the graph with the vertex at the top.



Edwin