#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]}