A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the price the widgets should be sold for y=-44x^2+1375x-6548. round to nearest cent for companys maximum profit.
we have the quadratic equation
y=-44x^2+1375x-6548
this is a vertical parabola open downward
the vertex is a maximum
the y-coordinate of the vertex represent the maximum profit
so
Convert the quadratic equation into vertex form
factor -44
y=-44(x^2-31.25x)-6548
Complete the square
y=-44(x^2-31.25x+244.14)-6548+10,742.19
y=-44(x-15.625)^2+4,194.19
therefore
the vertex is the point (15.63, 4,194.19)
the maximum profit is $4,194.19