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 has the equation $x = -\frac{b}{2a}$ for a quadratic function in standard form.

5 Must Know Facts For Your Next Test

1. The axis of symmetry always intersects the vertex of the parabola.
2. For a quadratic function $f(x) = ax^2 + bx + c$, the axis of symmetry can be found using $x = -\frac{b}{2a}$.
3. It helps to determine whether the parabola opens upwards or downwards based on the sign of coefficient $a$.
4. The axis of symmetry is crucial for finding the maximum or minimum value of a quadratic function.
5. Knowing the axis of symmetry helps in graphing parabolas accurately.

Review Questions

• What is the formula to find the axis of symmetry for a quadratic function?
• How does the axis of symmetry relate to the vertex of a parabola?
• Why is knowing the axis of symmetry important when graphing a quadratic function?

Related terms

Vertex:

The highest or lowest point on a parabola, located at $(h, k)$ where $h$ is given by $h = -\frac{b}{2a}$.

Parabola:

A symmetrical plane curve formed by all points equidistant from both a fixed point (focus) and a fixed straight line (directrix).

Quadratic Function:

A polynomial function of degree two, generally expressed as $f(x) = ax^2 + bx + c$ where $a \neq 0$.