Parabola Maximum and Minimum: Example 5

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) = -2x² + 8x + 9. With a = -2 being negative, the parabola opens downward and has a maximum value. The x-coordinate of the vertex is x = -b/(2a) = 2. The maximum y-value is f(2) = 17. Therefore, the maximum value is 17, occurring at x = 2. The vertex (2, 17) 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.