Parabola

Definition

A parabola is a symmetric curve that represents the graph of a quadratic function. It can open upward or downward depending on the sign of the quadratic coefficient.

5 Must Know Facts For Your Next Test

1. The standard form of a parabola's equation is $y = ax^2 + bx + c$.
2. The vertex form of a parabola's equation is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.
3. The axis of symmetry of a parabola in standard form $y = ax^2 + bx + c$ is given by $x = -\frac{b}{2a}$.
4. A parabola opens upward if the coefficient $a > 0$ and downward if $a < 0$.
5. The focus and directrix are key features of the parabolic shape, with every point on the parabola equidistant from both.

Review Questions

• What is the standard form of a quadratic equation representing a parabola?
• How do you find the vertex of a parabola given its equation in standard form?
• In which direction does a parabola open if the quadratic coefficient $a$ is negative?

Related terms

Vertex:

The highest or lowest point on a parabola, located at $(h, k)$ in vertex form.

Focus:

A fixed point used to define a parabola, located along the axis of symmetry.

Directrix:

A fixed line used to define a parabola; each point on the parabola is equidistant from this line and its focus.