SOLUTION: Thank you in advance for you help with this equation. I really appreciate it. Question 1 The total profit (in dollars) for sales of x rowing machines is given by P(x) = -0.2x^2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Thank you in advance for you help with this equation. I really appreciate it. Question 1 The total profit (in dollars) for sales of x rowing machines is given by P(x) = -0.2x^2       Log On


   

Question 23392: Thank you in advance for you help with this equation. I really appreciate it.
Question 1
The total profit (in dollars) for sales of x rowing machines is given by P(x) = -0.2x^2 + 300x - 200. What is the total profit if 500 are sold? For what value of x will the profit be at a maximum?
Question 2
Solve the equation by using the quadratic equation.
y^2 + 6y + 4 = 0
Question 3
Solve the equation
b+17/b^2-1 - 1/b+1 = b-2/b-1
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
#1: In place of "x" put 500. Then evaluate.
You have a quadratic with a=-0.2, b=300, c=-200
The max is at x=-b/2a = 300/0.4 = 7500
In place of "x" in the original equation put 7500 to
find the corresponding P(7500)
#2:a=1,b=6,c=4
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A1%2A4=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+-0.76393202250021
x%5B2%5D+=+%28-%286%29-sqrt%28+20+%29%29%2F2%5C1+=+-5.23606797749979

Quadratic expression 1x%5E2%2B6x%2B4 can be factored:
1x%5E2%2B6x%2B4+=+1%28x--0.76393202250021%29%2A%28x--5.23606797749979%29
Again, the answer is: -0.76393202250021, -5.23606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B4+%29

#3: Can't tell where your denominators end. Please
use parentheses.
Cheers,
Stan H.