- Because the leading coefficient of the parabola equation is negative, the vertex of the parabola is the highest point on the graph.First, determine the value of x that maximizes the profit by determining the coordinate of the vertex:x​=−2ab​=−2(−1)120​=60​- The coat manufacturer must sell 60 coats each day to earn a maximum profit for that day. Because the maximum profit corresponds to the y-coordinate of the vertex, substitute 60 for x in the parabola equation to find the corresponding value of y :y​=−602+120(60)−2,000=−3,600+7,200−2,000=1,600​The maximum profit is $1,600. You could also have arrived at the correct answer by changing the parabola equation to vertex form.