Parabola Maximum and Minimum: Example 2

Topic

Quadratics

Description

The maximum or minimum value of a parabola occurs at its vertex. For a parabola opening upward (a > 0), this point is a minimum. For a parabola opening downward (a < 0), it's a maximum. The vertex lies on the axis of symmetry.

For a quadratic function in standard form f(x) = ax² + bx + c, the x-coordinate of the vertex is given by x = -b/(2a), and the y-coordinate (maximum or minimum value) can be calculated by substituting this x-value into the original function.

In this example, we have f(x) = 5x² - 10x + 8. Since a = 5 is positive, the parabola opens upward and has a minimum value. The x-coordinate of the vertex is x = -b/(2a) =  1. The minimum y-value is f(1) = 3. Thus, the minimum value is 3, occurring at x = 1. The vertex (1, 3) lies on the axis of symmetry x = 1.

For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.