the graph of y= -x^2+5x-20 lies in which quadrants?

Question

can you please show the work and not only give me the answer

Answer 1

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.