Question 632691
coefficient of the x^2 term is negative, so it's an upside down parabola, vertex will be at the local maximum, which occurs when the derivative of y(x) = 0

y(x) = -x^2/4 - x/5

dy/dx (y(x)) = -x/2 - 1/5 

set equal to zero:

-x/2 - 1/5 = 0

-x/2 = 1/5

x = -2/5

The highest point on the upside down parabola, which is the vertex, occurs when x= -2/5

y(x) = -x^2/4 - x/5

y(-2/5) = (-1/4)(-2/5)^2  - (-2/5)/5

 =   (-1/4)(4/25) + 2/25

 =  -1/25 + 2/25 = 1/25

x = -2/5, y = 1/25

(-2/5, 1/25)