Finding the standard form of a parabola given directrix and vertex

The video tutorial explains how to find the standard form of a parabola's equation. It begins by introducing the concept and discussing how to choose the correct equation based on the given information. The instructor emphasizes the importance of graphing the vertex and directrix to determine the graph's orientation. The tutorial then covers how to calculate the value of P, which is the distance from the vertex to the focus. Finally, the instructor demonstrates how to write the equation in standard form, ensuring it aligns with the standard format.

What is the first step in determining which standard form equation to use for a parabola?

• Determine the orientation of the parabola.

• Plot the given information.

• Calculate the value of P.

• Identify the vertex and directrix.

How does the position of the directrix affect the orientation of a parabola?

• It determines whether the parabola opens up or down.

• It only affects the size of the parabola.

• It determines whether the parabola opens left or right.

• It has no effect on the orientation.

What is the significance of the value of P in a parabola's equation?

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

• It affects the height of the parabola.

• It is the distance from the vertex to the focus.

• It determines the width of the parabola.

How do you find the value of P for a parabola?

• By calculating the midpoint between the vertex and the directrix.

• By measuring the distance from the vertex to the focus.

• By calculating the midpoint between the vertex and the focus.

• By measuring the distance from the vertex to the directrix.

What is the final step in expressing a parabola's equation in standard form?

• Calculate the value of P.

• Determine the orientation of the parabola.

• Solve for Y in the equation.

• Identify the vertex and directrix.

Which formula is used when the parabola opens up or down?

• Y - K squared = 4P(X - H)

• X - H squared = 4P(Y - K)

• Y - K squared = 4P(Y - K)

• X - H squared = 4P(X - H)

What is the standard form of a parabola's equation when solved for Y?

• Y = AX squared + BX + C

• X = AY squared + BY + C

• Y = A(X - H) squared + K

• X = A(Y - K) squared + H