Parabola Maximum and Minimum: Example 9

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.

This example shows f(x) = 5x² + 20x + 9. With a = 5 being positive, the parabola opens upward and has a minimum value. The x-coordinate of the vertex is x = -b/(2a) = -2. The maximum y-value is f(-2) = -11. Therefore, the maximum value is -11, occurring at x = -2. The vertex (-2, -11) is on the axis of symmetry x = -2.

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