Mr. Kirkland October 15, 2013
Your school's Jazz Band is selling CDs as a fundraiser. The total profit (p) depends on the amount (x) that your band charges for each CD. THe equation p= -x^2 + 48x-300 models the profit of the fundraiser. What is the least amount, in dollars, you can charge for a CD to make a $100 profit?
Here are the formulas that are needed in order to complete the Jazz Band Word Problem.
Quadratic - Involving the second and no higher power of an unknown quantity or variable. - A quadratic Equation.
P= 100 is the number in order to make a profit. You also plug this number into the formula, p= -x^2+48x-300
The equation P= -x^2+48x-300 is what is needed in order to find the quadratic function, which is ax^2+bx+c.
Here is where the "plug in" is put into affect, in order to solve the problem. This is also where the Quadratic Function is formed.
Now that the quadratic function is present, it can now be plugged into the quadratic formula, which is shown.
As you can see, here is where the "plug in" method has been used again in order to solve the Quadratic Function. Here, is where you will get your answer.
Even though the answer came out as a decimal, it can be converted into an amount. The solution was a 10.734 or 37.266. Our word problem asked us to look for the least amount in dollars, you could charge for a CD in order to make a profit. The least amount was 10.734 = $10.74. Now the Jazz Band Quadratic Word Problem is complete.