Please show your work and explain!

Question

Find the maximum or minimum value of the quadratic function –3x² – 30x – 73 by completing the square.

Answer 1

take the derivative and set it equal to zero

-6x -30 = 0

x = 5

substitute x=5 into the quadratic polynomial

-3(x^2)-30x - 73 =

-3(25)-30(5) -73 =

-75 -150 -73 = -298 or the point (5,-298) is the maximum point and vertex of the parabola

there is no minimum, or no real number for the minimum. It approaches negative infinity

(although negative infinity while just a limit for real numbers, is a "surreal number" and you could call it the global minimum, but people generally don't do that)