Given the vertex and directrix, learn to write the standard form of a parabola

The video tutorial explains how to write the standard form of a parabola equation using a given vertex and directrix. It covers graphing the directrix, understanding the relationship between the focus and directrix, and calculating the focus. The tutorial concludes with formulating and simplifying the parabola equation.

What is the first step in writing the standard form of a parabola's equation?

• Identify the axis of symmetry

• Graph the parabola

• Calculate the distance to the focus

• Determine the parabola's orientation

How is the focus of a parabola related to the vertex and directrix?

• It is the same distance from the vertex as the directrix but in the opposite direction

• It is twice the distance from the vertex to the directrix

• It is equidistant from the vertex and the directrix

• It is always below the directrix

What is the value of P if the distance from the vertex to the directrix is 5?

• P = -5

• P = 0

• P = 5

• P = 10

Which form does the equation of a parabola with a vertical axis of symmetry take?

• Y - K = 4P(X - H)^2

• X - H = 4P(Y - K)^2

• X - H^2 = 4P(Y - K)

• Y - K^2 = 4P(X - H)

What values are substituted for H and K in the equation X - H^2 = 4P(Y - K)?

• H = 0, K = 0

• H = 1, K = 8

• H = 8, K = 1

• H = 5, K = 5

What is the final simplified form of the equation after expanding and distributing?

• Y = 20X^2 - 2X + 161

• Y = 1/10 X^2 - 1/20 X + 161/10

• Y = 1/20 X^2 - 1/10 X + 161/20

• Y = X^2 - 2X + 161

Why is it important to reduce the equation to its simplest form?

• To make it easier to solve for X

• To verify the accuracy of calculations

• To ensure it fits the standard form

• To make it easier to graph