At Otto’s egg farm, Otto has found that when he charges $0.05 per egg, he sell so many eggs that he cannot keep up with the demand and has zero profit. When he charges $0.17 per egg, he sells so few eggs that he has to throw some out and is also left with zero profit. Currently he charges $0.15 per egg and has a profit of $124 per day. Let p(c)be his profit in dollars, from charging c dollars per egg. Assume that p(c) is a quadratic function of c. Find a formula for p(c)
What should Otto charge to maximize his profit? What will that profit be?

a) P(c) = xc² + yc + z, and P(.15) = $124, P(.05) = 0, P(.17) = 0. Thus:

(#1) .0225x + .15y + z = 124

(#2) .0025x + .05y + z = 0

(#3) .0289x + .17y + z = 0

Subtracting #2 from #3: (#4) .0264x + .12y = 0

Subtracting #2 from #3: (#5) .02x + .1y = 124

Subtracting 1.2×#5 from #4: .0024x = -148.8 → x= -62000

Using this value of x in #5: -1240 + .1y = 124 → y = 13640

Using x and y in #1: -1395 + 2046 + z = 124 → z = -527

P(c) = -62000c² + 13640c - 527

b) To find the maximum of P(c), find a such that P'(a) = 0

-124000c + 13640 = 0

c = .11

At this price, his profit would be $223.20

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct

where is the graph? need more info