What is how to find axis of symmetry?

Here's how to find the axis of symmetry for different types of functions:

1. For Quadratic Functions (Parabolas):

• Standard Form: If the quadratic function is in the form f(x) = ax² + bx + c, the axis of symmetry is a vertical line defined by the equation:

  • x = -b / 2a
  • This formula finds the x-coordinate of the parabola's vertex. The axis of symmetry passes through the vertex.

• Vertex Form: If the quadratic function is in the form f(x) = a(x - h)² + k, the axis of symmetry is simply:

  • x = h
  • Here, (h, k) represents the vertex of the parabola.

2. Using the Roots/Zeros of a Quadratic Function:

• If you know the roots (x-intercepts) of the quadratic function (let's call them x₁ and x₂), the axis of symmetry is located exactly in the middle of these roots:
  • x = (x₁ + x₂) / 2

3. Understanding the Concept:

• The axis%20of%20symmetry is a line that divides the parabola into two mirror-image halves. It always passes through the vertex.
• For parabolas, the axis of symmetry is always a vertical line of the form x = constant.

Key Concepts to Remember:

• Vertex: The highest or lowest point on the parabola.
• Axis%20of%20Symmetry: The line that divides the parabola into two symmetrical halves.