Parabola

Definition

A parabola is a symmetric curve formed by the set of all points in a plane that are equidistant from a given point called the focus and a given line called the directrix. It is commonly represented by the quadratic function $y = ax^2 + bx + c$.

5 Must Know Facts For Your Next Test

1. The vertex form of a parabola's equation is $y = a(x-h)^2 + k$, where $(h, k)$ is the vertex.
2. The axis of symmetry of a parabola given by $y = ax^2 + bx + c$ is $x = -\frac{b}{2a}$.
3. In parametric equations, a parabola can be represented as $x = t$ and $y = at^2 + bt + c$.
4. The focus of a parabola described by $y = ax^2 + bx + c$ can be found using the formula $(h, k+\frac{1}{4a})$, where $(h,k)$ is the vertex.
5. A parabola opens upwards if $a > 0$ and downwards if $a < 0$ in the equation $y = ax^2 + bx + c$.

Review Questions

• What is the standard form of a parabolic equation?
• How do you determine the direction in which a parabola opens?
• What are the coordinates of the vertex for the quadratic function $y = ax^2 + bx + c$?

Related terms

Vertex: The highest or lowest point on the graph of a parabola, located at $(h, k)$ in its vertex form.

Directrix: A fixed line used in describing a parabola; every point on the parabola is equidistant from this line and its focus.

Focus: A fixed point used with the directrix to define a parabola; all points on the parabola are equidistant from this point and the directrix.