Learning Goal: To understand and use quadratic relationships. Two quantities x and y are said to have a quadratic relationship if y is proportional to the square of x. We write the mathematical relationship as y=Ax2 where A is a constant or, in words, y is proportional to x2. The graph of a quadratic relationship is a parabola. SCALING If x has the initial value x1, then y has the initial value y1=A(x1)2. Changing x from x1 to x2 changes y from y1 to y2. The ratio of y2 to y1 is y2y1=A(x2)2A(x1)2=(x2x1)2. The ratio of y2 to y1 is the square of the ratio of x2 to x1. If y is a quadratic function of x, a change in x by some factor changes y by the square of that factor: If you increase x by a factor of 2 , you increase y by a factor of 22=4 . If you decrease x by a factor of 3 , you decrease y by a factor of 32=9 . Generally, we can say that: Changing x by a factor of c changes y by a factor of c2.