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Maximum and minimum
- 1. Maximum and Minimum using Quadratic Functions and not too much algebra! These slides were prepared for management mathematics students, some of whom had no algebra at the start of the course. y = x族 y = x族 10 10 y = x族 9 8 10 8 7 6 6 5 5 4 4 0 2 3 -5 0 5 2 0 -5 1 -5 -2 0 5 0 -4 -2 -1 0 2 4
- 2. Quadratic Functions The graphs of many equations are called functions. In economics and finance we are often interested in where the minimum value (turning point) is (the X ordinate) and what the minimum value is (the Y ordinate). If the graph is inverted then we are looking for the maximum value.
- 3. The basic equation for a quadratic function is y = x2. The minimum value is found at x = 0 and the minimum value is y = 0 y = x族 10 9 8 7 6 5 4 3 2 1 0 -4 -2 -1 0 2 4
- 4. A negative in front of the x2 inverts the graph. The maximum value is found at x = 0 and the maximum value is y = 0. y = -x族 1 0 -4 -3 -2 -1 -1 0 1 2 3 4 -2 -3 -4 -5 -6 -7 -8 -9 -10
- 5. y = x族 - 4 6 5 4 3 2 1 0 -4 -3 -2 -1 0 1 2 3 4 -1 -2 -3 -4 -5
- 6. A constant inserted inside the bracket slides the graph along the X axis in the Opposite direction. The minimum value is found at x = 2 and the minimum value is y = 0. y = (x - 2)族 10 9 8 7 6 5 4 3 2 1 0 -2 0 2 4 6 -1
- 7. y = (x + 3)族 - 2 8 7 6 5 4 3 2 1 0 -7 -5 -3 -1 1 3 -1 -2 -3