6.) the following function represents the profit p(n) in dollars that a concert promoter makes by selling tickets for n dollars each:
p(n)=-250n^2+3,250n-9,000

part a: what are the zeroes of the above function and what do they represent? show your work.

part b: find the maximum profit by completing the square of the function p(n ). show the steps of your work.

part c: what is the axis of symmetry of the function p(n )?

For Part A, what to do first is to equate the given equation to zero in order to find your x intercepts (zeroes)

0=-250n^2+3,250n-9,000 after factoring out, we get

-250(n-4)(n-9) and these are your zero values.

For Part B, you need to square the function from the general equation Ax^2+Bx+C=0. So to do that, we use the equated form of the equation 0=-250n^2+3,250n-9,000 and in order to have a positive value of 250n^2, we divide both sides by -1

250n^2-3,250n+9,000=0

to simplify, we divide it by 250 to get n^2-13n+36=0 or n^2-13n = -36 (this form is easier in order to complete the square, ax^2+bx=c)

in squaring, we need to apply (b/2)^2 to both sides where our b is -13 so,
(-13/2)^2 is 169/4

so the equation now becomes n^2-13n+169/4 = 25/4 or to simplify, we apply the concept of a perfect square binomial, so the equation turns out like this 

(n-13/2)^2 = 25/4 then to find the value of n, we apply the square root to both sides to obtain n-13/2 = 5/2 and n is 9. This gives us the confirmation from Part A. 

For Part C, since the function is a binomial so the graph is a parabola. The axis of symmetry would be x=5.

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