Maximum point and minimum point of a 2nd degree function

Every expression in the form y = ax² + bx + c or f (x) = ax² + bx + c, with a, b, and c real numbers, where a ≠ 0, is called 2nd degree function. The graphical representation of a 2nd degree function is given through a parable, which can have the concavity facing up or down. Look:

To determine the maximum point it's the minimum point of a 2nd degree function, just calculate the vertex of the parabola using the following mathematical expressions:

O maximum pointthe and the minimum point they can be attributed to various situations present in other sciences, such as Physics, Biology, Administration, Accounting, among others.
Physics: uniformly varied movement, projectile launch.
Biology: in the analysis of the photosynthesis process.
Administration: establishing leveling points, profit and loss.
Examples
1 – In the function y = x² - 2x +1, we have that a = 1, b = -2 and c = 1. We can verify that a > 0, so the parabola has a concavity facing upwards, having a minimum point. Let's calculate the coordinates of the vertex of the parabola.

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The vertex coordinates are (1, 0).

2 – Given the function y = -x² -x + 3, we have that a = -1, b = -1 and c = 3. We have a < 0, so the parabola has a downward-facing concavity having a maximum point. The vertices of the parabola can be calculated as follows:

The vertex coordinates are (-0.5; 3,25).
We conclude that the vertex of the parabola must be considered a remarkable point, due to its importance in the construction of the graph of a 2nd degree function and its relationship with the maximum and minimum value points.

by Mark Noah
Graduated in Mathematics

See more!

2nd degree equation
Resolution method.

2nd degree function
Definition, properties and graph.

High School Function - Roles - Math - Brazil School

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SILVA, Marcos Noé Pedro da. "Maximum point and minimum point of a 2nd degree function"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/maximo-minimo.htm. Accessed on July 27, 2021.