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

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.

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