Finding the Vertex and Axis of Symmetry for a Parabolic Equation | Step-by-Step Guide

Finding the axis of symmetry, “AoS”. f(x)=a(x-h)^2+k

The axis of symmetry (AoS) is a line that divides a parabolic graph into two symmetric halves

The axis of symmetry (AoS) is a line that divides a parabolic graph into two symmetric halves. In the equation you provided, f(x) = a(x – h)^2 + k, the values of h and k represent the vertex coordinates of the parabola. The vertex is the point where the parabola reaches its highest or lowest point, also known as the maximum or minimum point.

To find the axis of symmetry, you need to determine the x-value of the vertex, which is represented by h in the equation. The equation (x – h) signifies the distance from any point on the parabola to the vertex.

To find the vertex and the axis of symmetry, follow these steps:

1. Identify the values of h and k: In your equation, a represents the coefficient in front of the squared term, (x – h)^2, whereas h and k are constants that represent the vertex coordinates.

2. The x-coordinate of the vertex (h) can be found using the formula: h = -b / (2a). In your equation, since there is no linear term (x), b is equal to zero.

3. If you know the x-coordinate of the vertex (h), you can substitute it back into the equation to find the y-coordinate (k). This will give you the vertex coordinates (h, k).

4. The axis of symmetry is a vertical line passing through the vertex. Its equation is x = h, where h represents the x-coordinate of the vertex that you found earlier.

By following these steps, you can determine the vertex coordinates and the equation of the axis of symmetry for a parabola defined by the given equation.

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