Here is another illustration:
Imagine that you are asked to calculate the dimensions of the rectangular card board
you will need to make a picture frame whose area should be 12 square inches. You are
told that the height of the frame should be 1 inch lesser than the width of the frame due
to some space constraint.
Let width = x inches then height = x - 1 inches.
Area of the frame = width ´ height Þ 12 = x(x - 1)
x^2 - x - 12 = 0
x^2 + 3x - 4x - 12 = 0
x(x + 3) - 4(x + 3) = 0
(x + 3)(x - 4) = 0
x = {-3, 4}
But width can not be -3.
Width = 4 inches and height = 4 - 1 = 3 inches.
Thus, we have the quadratic function, A(x) = y = x^2 - x for the area of the cardboard.
x = Width of the cardboard and y = Area
When x = 4, y = 12 and when x = 5, y = 20.
Tutor
Masters Degree