Key Concepts & Glossary
Key Equations
Parabola, vertex at origin, axis of symmetry on x-axis | |
Parabola, vertex at origin, axis of symmetry on y-axis | |
Parabola, vertex at , axis of symmetry on x-axis | |
Parabola, vertex at , axis of symmetry on y-axis |
Key Concepts
- A parabola is the set of all points in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix.
- The standard form of a parabola with vertex and the x-axis as its axis of symmetry can be used to graph the parabola. If , the parabola opens right. If , the parabola opens left.
- The standard form of a parabola with vertex and the y-axis as its axis of symmetry can be used to graph the parabola. If , the parabola opens up. If , the parabola opens down.
- When given the focus and directrix of a parabola, we can write its equation in standard form.
- The standard form of a parabola with vertex and axis of symmetry parallel to the x-axis can be used to graph the parabola. If , the parabola opens right. If , the parabola opens left.
- The standard form of a parabola with vertex and axis of symmetry parallel to the y-axis can be used to graph the parabola. If , the parabola opens up. If , the parabola opens down.
- Real-world situations can be modeled using the standard equations of parabolas. For instance, given the diameter and focus of a cross-section of a parabolic reflector, we can find an equation that models its sides.
Glossary
- directrix
- a line perpendicular to the axis of symmetry of a parabola; a line such that the ratio of the distance between the points on the conic and the focus to the distance to the directrix is constant
- focus (of a parabola)
- a fixed point in the interior of a parabola that lies on the axis of symmetry
- latus rectum
- the line segment that passes through the focus of a parabola parallel to the directrix, with endpoints on the parabola
- parabola
- the set of all points in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix