Understanding the Axis of Symmetry | Key Information for Graphs and Shapes

axis of symmetry

The axis of symmetry is a line that divides a symmetrical shape or graph into two equal halves

The axis of symmetry is a line that divides a symmetrical shape or graph into two equal halves. In mathematics, it is often used to describe the symmetry of a graph of a function or a geometric figure.

For a quadratic function in the form of f(x) = ax^2 + bx + c, the axis of symmetry is a vertical line given by the equation x = -b / (2a). This line divides the parabolic graph into two symmetric halves. The vertex of the parabola lies on this axis, which is the point where the graph reaches its minimum or maximum value.

For example, consider the quadratic function f(x) = x^2. The graph of this function is a symmetrical U-shaped curve. The axis of symmetry is the vertical line x = 0, and it divides the graph into two equal halves. The vertex of the graph is located at (0,0), which is also the minimum point of the graph.

In geometry, the axis of symmetry is used to describe the line that divides a two-dimensional shape into two congruent halves. For example, a square has four lines of symmetry, each being an axis of symmetry that divides it into two equal parts.

Understanding the axis of symmetry is crucial in analyzing symmetry properties of functions and shapes, as it provides key information about the symmetry and behavior of the graph or figure.

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