#y=-25x^2-30x# is a quadratic equation in standard form, #ax^2+bx+c#, where #a=-25, b=-30, and c=0#. The graph of a quadratic equation is a parabola.
The vertex of a parabola is its minimum or maximum point. In this case it will be the maximum point because a parabola in which #a<0# opens downward.
Finding the Vertex
First determine the axis of symmetry, which will give you the #x# value. The formula for the axis of symmetry is #x=(-b)/(2a)#. Then substitute the value for #x# into the original equation and solve for #y#.
#x=-(-30)/((2)(-25))#
Simplify.
#x=(30)/(-50)#
Simplify.
#x=-3/5#
Solve for y.
Substitute the value for #x# into the original equation and solve for #y#.
#y=-25x^2-30x#
#y=-25(-3/5)^2-30(-3/5)#
Simplify.
#y=-25(9/25)+90/5#
Simplify.
#y=-cancel25(9/cancel25)+90/5#
#y=-9+90/5#
Simplify #90/5# to #18#.
#y=-9+18#
#y=9#
The vertex is #(-3/5,9)#.
graph{y=-25x^2-30x [-10.56, 9.44, 0.31, 10.31]}