Assess: Equations of Parabolas (11/8/24)

Front

What is a parabola?

Back

A parabola is a symmetric curve formed by the intersection of a cone with a plane parallel to its side. It can be 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?

Back

The standard form of a parabola that opens upwards is given by the equation: (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 focus of a parabola?

Back

The focus of a parabola is a fixed point located inside the curve, which is equidistant from any point on the parabola to the directrix.

Front

What is the directrix of a parabola?

Back

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

Front

How do you find the vertex of a parabola given its equation in standard form?

Back

For the equation (x-h)² = 4p(y-k), the vertex is at the point (h,k).

Front

What is the relationship between the focus and directrix of a parabola?

Back

The focus and directrix are equidistant from any point on the parabola, which defines the shape of the parabola.

Front

What is the equation of a parabola that opens to the right?

Back

The standard form of a parabola that opens to the right is given by the equation: (y-k)² = 4p(x-h), where (h,k) is the vertex and p is the distance from the vertex to the focus.

Front

How do you determine the coordinates of the focus from the equation of a parabola?

Back

For the equation (x-h)² = 4p(y-k), the focus is located at (h, k+p). For (y-k)² = 4p(x-h), the focus is at (h+p, k).

Front

What is the significance of the value 'p' in the equations of parabolas?

Back

The value 'p' represents the distance from the vertex to the focus and also from the vertex to the directrix. It determines the width and direction of the parabola.

Front

How can you find the directrix from the equation of a parabola?

Back

For the equation (x-h)² = 4p(y-k), the directrix is the line y = k - p. For (y-k)² = 4p(x-h), the directrix is the line x = h - p.