Properties and Equations of Parabolas

The video tutorial explains how to find the equation of a parabola given its focus and directrix. It covers graphing the parabola, determining the vertex as the midpoint between the focus and directrix, and identifying the parabola's orientation. The tutorial then guides through formulating the equation using the vertex and focus, converting it into standard and general forms, and simplifying the equation.

What is the first step in finding the equation of a parabola given its focus and directrix?

• Calculate the distance between the focus and directrix.

• Graph the parabola using the given focus and directrix.

• Find the midpoint between the focus and directrix.

• Determine the direction the parabola opens.

What is the equation of the directrix given in the problem?

• x = 4

• y = 4

• x = -4

• y = -4

What is the focus of the parabola in the given problem?

• (-3, -2)

• (-3, 2)

• (3, 2)

• (3, -2)

Where is the focus located in relation to the parabola?

• Inside the parabola

• On the directrix

• Outside the parabola

• At the vertex

How do you calculate the vertex of a parabola?

• By finding the midpoint between the focus and directrix

• By using the formula x^2 = 4py

• By calculating the distance from the focus to the directrix

• By determining the direction the parabola opens

What is the distance between the focus and the directrix?

• 6

• 12

• 9

• 3

What is the midpoint between the focus and the directrix?

• (-3, 1)

• (-3, -1)

• (3, 1)

• (3, -1)

What is the direction of a parabola if the focus is below the directrix?

• Opens to the right

• Opens downward

• Opens to the left

• Opens upward

Which formula is used for a parabola that opens downward?

• x^2 = -4py

• y^2 = 4px

• x^2 = 4py

• y^2 = -4px

What are the values of h and k in the vertex form of a parabola?

• h = 3, k = -1

• h = -3, k = 1

• h = -1, k = 3

• h = 1, k = -3