More 12.2 Review: Parabolas (Conic Sections)

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is defined as the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix).

Front

What is the standard form of a parabola that opens upwards or downwards?

Back

The standard form is (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus.

Front

What is the standard form of a parabola that opens sideways?

Back

The standard form is (y - k)² = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its orientation.

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola, where all the reflected rays converge.

Front

What is the directrix of a parabola?

Back

The directrix is a fixed line used in the definition of a parabola, which is perpendicular to the axis of symmetry.

Front

What is the focal width of a parabola?

Back

The focal width is the distance between the points on the parabola that are directly above and below the focus.

Front

How do you find the focus of a parabola given its equation?

Back

For a parabola in the form (y - k)² = 4p(x - h), the focus is located at (h + p, k) if it opens right, or (h - p, k) if it opens left.

Front

How do you find the directrix of a parabola given its equation?

Back

For a parabola in the form (y - k)² = 4p(x - h), the directrix is the line x = h - p if it opens right, or x = h + p if it opens left.

Front

What is the axis of symmetry of a parabola?

Back

The axis of symmetry is a vertical or horizontal line that divides the parabola into two mirror-image halves.