Write the equation of a parabola given the directrix

The video tutorial explains how to find the standard form of a parabola with a vertex at the origin and a directrix at y = -1. It covers graphing the parabola to determine its axis of symmetry, calculating the P value, and finalizing the standard form equation. The tutorial emphasizes understanding the relationship between the vertex, focus, and directrix to determine the parabola's direction and form.

What information is given about the parabola in the problem?

• The vertex is at (0, 0) and the directrix is at y = -1.

• The vertex is at (1, 1) and the directrix is at y = -1.

• The vertex is at (0, 0) and the directrix is at y = 1.

• The vertex is at (1, 1) and the directrix is at y = 1.

How does the parabola open in relation to the directrix?

• Parallel to the directrix.

• In the opposite direction of the directrix.

• In the same direction as the directrix.

• Perpendicular to the directrix.

What is the value of P if the directrix is at y = -1 and the vertex is at (0, 0)?

• P = 0

• P = 2

• P = -1

• P = 1

What is the standard form of the equation for a parabola with a vertical axis of symmetry?

• Y^2 = 4P(X - H)

• X - H = 4P(Y - K)^2

• Y - K = 4P(X - H)^2

• X^2 = 4P(Y - K)

How do you determine the focus of a parabola given the vertex and directrix?

• By dividing the distance P by the vertex.

• By multiplying the distance P with the vertex.

• By subtracting the distance P from the vertex.

• By adding the distance P to the vertex.