what is the vertex of -x^2+500x-25000

Question

what is the number of units that gives maximum profit is x=

 

Answer 1

Rewrite as -25000-(x²-500x). This can be written: -25000-(x²-500x+62500-62500).

This is the same as -25000-(x-250)²+62500=37500-(x-250)².

The squared term has a minimum value of 0 when x=250, and the profit is maximum at 37500. This is the vertex (250,37500).