SOLUTION: Your class is selling boxes of flower seeds as a fundraiser the total profit P depends on the amount X that your class charges for each box of seeds the Quetion P = -0.5 X^2+36x-1

Question 991202: Your class is selling boxes of flower seeds as a fundraiser the total profit P depends on the amount X that your class charges for each box of seeds the Quetion P = -0.5 X^2+36x-103 models the profit of the fundraiser what's the smallest amount in dollars that you can charge and make a profit of at least $419?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your answer appears to be:
20.125492133612454
you can solve it by use of the quadratic formula, or by graphing.
use of the quadratic formula requires the following transformation.
let y = profit
your equation is y = -.5x^2 + 36x - 103
set y = 419 to get:\
419 = -.5x^2 + 36x - 103
subtract 419 from both sides of the equation to get:
0 = -.5x^2 + 36x - 522
that in standard quadratic form of 0 = ax^2 + bx + c, where:
a = -.5
b = 36
c = -522
you just plug those numbers in the quadratic formula and you will get your answer.
you can also solve it graphically.
two ways to do it.
one way is to use the transformed equation and look for the zero crossing points.
that equation would be y = -.5x^2 + 36x - 522
the other way is to graph two equations and look for the intersection points.
those equations are:
y = -.5x^2 + 36x - 103
y = 419
the following graphs show you the results of both methods.

$$$

if you need to learn how to use the quadratic formula, it can be found here:

http://www.regentsprep.org/regents/math/algtrig/ate3/quadformula.htm

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