Understanding the Axis of Symmetry in Quadratic Functions | Formula and Example

Axis of Symmetry

The axis of symmetry is a line that divides a figure into two equal halves, such that if you fold the figure along that line, the two halves would perfectly overlap

The axis of symmetry is a line that divides a figure into two equal halves, such that if you fold the figure along that line, the two halves would perfectly overlap. In mathematics, the axis of symmetry is commonly discussed in relation to graphs of quadratic functions.

For a quadratic function in the form of f(x) = ax^2 + bx + c, the axis of symmetry can be found using the formula: x = -b / (2a). This formula gives you the x-coordinate of the vertex of the quadratic function, which is the point on the graph where it reaches its maximum or minimum value.

To illustrate the concept, let’s consider the quadratic function f(x) = x^2 – 4x + 3. We can find the axis of symmetry by using the formula: x = -b / (2a) = -(-4) / (2*1) = 4 / 2 = 2. Therefore, the axis of symmetry for this quadratic function is x = 2.

This means that if we were to plot the graph of this quadratic function, the line x = 2 would be the axis of symmetry. Any point on the graph that lies on one side of this line has an exact reflection on the other side, as the graph is symmetric with respect to the axis of symmetry.

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