Quadratic Function
Given a quadratic function of the form:
[tex]y=ax^2+bx+c[/tex]The vertex of the parabola that represents the function is located at the x-coordinate:
[tex]x=-\frac{b}{2a}[/tex]If the value of a is positive, the function has a minimum value at the vertex and if a is negative, the function has a maximum value at the vertex.
We are given the amount of profit y, as a function of the selling price of each widget x:
[tex]y=-2x^2+105x-773[/tex]Here: a=-2, b=105, c=-773. Calculating the x-coordinate of the vertex:
[tex]x=-\frac{105}{2\cdot(-2)}=\frac{105}{4}=26.25[/tex]Now substitute in the function:
[tex]y=-2(26.25)^2+105\cdot26.25-773=605.125[/tex]The maximum amount of profit the company can make is $605
