What is the axis of symmetry for f(x) = -5x^2-20x-10

The axis of symmetry is a vertical line, and it can be found several ways--the easiest way in your case is to use this equation:

x = -b/2a

this helps you find the x value of your vertex; the axis of symmetry crosses your vertex. all you have to do is find the x value, because the equation of a vertical line is x =

x = (20/2(-5))
x = 20/-10
x = -2

the equation for your axis of symmetry is x = -2, which is a vertical line at -2 on the x-axis