# What is the axis of symmetry of the function f(x) = -(x + 9)(x – 21)?

Updated on January 19, 2024

Answer: The axis of symmetry is x = 6.

## Understanding the Axis of Symmetry in Quadratic Functions

The axis of symmetry of a quadratic function can be found by averaging the x-values of the x-intercepts or by using the formula x = -b/2a. For f(x) = -(x + 9)(x – 21), the x-intercepts are -9 and 21. Averaging these gives (-9 + 21)/2 = 6. The axis of symmetry is a vertical line through this average, x = 6, which divides the parabola into two mirror-image halves. This concept is fundamental in algebra and geometry for analyzing the properties of quadratic functions and their graphs.

## FAQ on Understanding the Axis of Symmetry in Quadratic Functions

### How do you find the axis of symmetry?

Average the x-values of the x-intercepts or use x = -b/2a.

### What does the axis of symmetry represent?

It represents a vertical line where the quadratic function’s graph is mirrored.

### How is the axis of symmetry related to the vertex?

The axis of symmetry passes through the vertex of the parabola.