y = -x^2 + 5x - 20
y = -(x^2 - 5x) - 20
y = -(x - 5/2)^2 + (25/4) - 20
y = -(x - 5/2)^2 - 55/4
From the above, we can see that y <= -55/4 < 0 for all real values of x.
Thus, the graph will always be below the x-axis.
Hence, the graph will lie in the 3rd and 4th quadrants.