How to I find the maximum algebraically?

Question

y=-5x^2-8x+2

Answer 1

The maximum will be the vertex. This will lie on the line of symmetry, which is always x = -b/(2a).
In this case, b = -8 and a = -5, so the line of symmetry is
x = -(-8)/(2*-5)
x = -8/10
x = -4/5

Plug this into the equation and solve for y. This will be your maximum value.

I hope this helps!

Answer 2

If the quadradic is ax^2+bx+c, the maximum occurs at 0=2ax+b or x=-b/2a.