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

axis of symmetry

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

The axis of symmetry is an imaginary line that divides a symmetrical shape or graph into two equal halves. In mathematics, the concept of axis of symmetry is commonly associated with quadratic functions or parabolas.

For a quadratic function of the form y = ax^2 + bx + c, the axis of symmetry can be determined using the formula x = -b/2a. This formula tells us that the axis of symmetry is a vertical line passing through the vertex of the parabola, which is the highest or lowest point on the graph.

To find the axis of symmetry, we can follow these steps:
1. Identify the values of a, b, and c in the quadratic function. These represent the coefficients of the quadratic equation.
2. Use the formula x = -b/2a. Substitute the values of a and b into the formula.
3. Calculate the value of x, which represents the x-coordinate of the axis of symmetry.

For example, let’s consider the quadratic function y = 2x^2 + 4x + 1.
To find the axis of symmetry, we need to use the formula x = -b/2a.
In this case, a = 2 and b = 4. Substituting these values into the formula, we get:
x = -4/(2*2) = -4/4 = -1.

Therefore, the axis of symmetry for this quadratic function is x = -1. This means that the graph of the function is symmetric with respect to the vertical line x = -1.

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