SOLUTION: John owns a hotdog stand. He has found that his profit is represented by the equation {{{P(x)= -x^2+56x+73}}},, where x is the number of hotdogs. How many hotdogs must he sell to m

Question 114677: John owns a hotdog stand. He has found that his profit is represented by the equation ,, where x is the number of hotdogs. How many hotdogs must he sell to make a profit?
P(x)=x^2+56x+73
Choices:
45 hotdogs
28 hotdogs
56 hotdogs
73 hotdogs
Thank you.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
The question is not phrased properly.
One formula has -x^2 in it and the repeat of it has x^2.
The question should be "how many hot dogs must he sell to maximize his profit".

x=-1.27456, x=57.27456 quadratic formula (see below)
(-1.27456+57.27456)/2=28 maximum of the graph
By checking the next graph you can see that he can make a profit by selling between 1 and 57 hot dogs and he makes a maximum profit at 28 hot dogs.

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=3428 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -1.27456233660889, 57.2745623366089. Here's your graph:

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