To find the price that produces profit, begin by finding the price in which the profit is zero.
Price ($): 9.25 < x < 313.752
Practice makes perfect
To find the price of the Web sites that produces profit, we will begin by finding the price of the Web sites in which the profit is zero. We will begin by substituting P(x)=0 in the given function. Then we will continue with writing the terms on the left-hand side.
Now we will solve the equation. Because the leading coefficient is not 1 and we cannot factor it out, we will use the Quadratic Formula to find the zeros of the equation.
ax^2+ bx+ c=0 ⇔ x=- b± sqrt(b^2-4 a c)/2 a
In our case, a= 16, b= -368, and c= 2035. Let's substitute these values into the formula and find the zeros.
Therefore, we have two roots as x=9.25 and x=13.75. Notice that the leading coefficient is negative. This means that the graph of the function opens downward and it has a maximum value. Therefore, P(x) is positive for 9.25 < x < 13.75. When the price is between this range, the company will earn profit.
