Axis of symmetry

Definition

The axis of symmetry is a vertical line that divides a parabola into two mirror-image halves. It passes through the vertex of the parabola, and its equation is $x = h$ where $h$ is the x-coordinate of the vertex.

5 Must Know Facts For Your Next Test

1. For a quadratic function in standard form $y = ax^2 + bx + c$, the axis of symmetry can be found using the formula $x = -\frac{b}{2a}$.
2. The axis of symmetry is always perpendicular to the directrix of a parabola.
3. In vertex form $y = a(x - h)^2 + k$, the axis of symmetry is given by the equation $x = h$.
4. The axis of symmetry helps in identifying key properties such as the maximum or minimum point (vertex) of a quadratic function.
5. By reflecting points across the axis of symmetry, you can generate additional points that lie on the parabola.

Review Questions

• What is the formula for finding the axis of symmetry for a quadratic function in standard form?
• How does knowing the axis of symmetry help in graphing a quadratic function?
• If you have a quadratic function in vertex form, how do you determine its axis of symmetry?

Related terms

Vertex: The highest or lowest point on a parabola, located on the axis of symmetry.

Parabola: A symmetric curve shaped like an open bowl which can represent various quadratic functions.

Standard Form: $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants. This form makes it easier to apply certain algebraic methods to analyze quadratic functions.