Understanding the Axis of Symmetry in Quadratic Functions: A Visual Explanation with Formula and Example

axis of symmetry

The axis of symmetry is a concept in mathematics that applies specifically to quadratic functions

The axis of symmetry is a concept in mathematics that applies specifically to quadratic functions. A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

The axis of symmetry is a vertical line that divides the parabola created by the quadratic function into two mirror image halves. It is a line of symmetry for the parabola. The equation of the axis of symmetry can be found using the formula x = -b / (2a).

To understand this concept better, let’s go through an example. Suppose we have the quadratic function f(x) = 2x^2 – 4x + 1. We can find the axis of symmetry for this function by using the formula x = -b / (2a).

By comparing the given quadratic function with the standard form for a quadratic function, we can determine that a = 2 and b = -4. Plugging these values into the formula, we find:

x = -(-4) / (2 * 2)
x = 4 / 4
x = 1

Therefore, for the given quadratic function f(x) = 2x^2 – 4x + 1, the axis of symmetry is x = 1.

Visually, this means that if we were to draw the graph of the quadratic function, the axis of symmetry would be a vertical line passing through the point (1, 0). The parabola would be symmetric with respect to this line, meaning that if we were to reflect any point on one side of the axis of symmetry across the line, we would obtain a corresponding point on the other side.

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