Find Maximum Product for Two Numbers With a Given Sum

Among all pairs of numbers whose sum is 22, find a pair whose product is as large as possible. What is the maximum product? Let x= the first number, y= the second number, P= product. The information about the sum gives the equation x+y=22, which is solve for y in terms of x. Then the product can be found using P=xy=x(22-x). This is a quadratic function that opens down and the maximum product is located at the vertex of this parabola.

Timestamps:
0:00 Introduction
0:41 Product Equation
1:12 Sum Equation
3:06 Quadratic Function
4:00 Find Vertex