Understanding Parabolas

The video tutorial explains how to graph parabolas by finding the value of p, determining the orientation based on x^2 or y^2, and plotting the vertex, focus, and directrix. It covers two examples: one with x^2 = 12y, which faces upwards, and another with -8x = y^2, which faces left. The tutorial also explains how to use the focal width to plot additional points on the parabola.

What is the first step in graphing a parabola?

• Determine the direction

• Find the value of p

• Plot the directrix

• Find the vertex

How do you determine the direction a parabola faces?

• By the sign of p

• By the value of the directrix

• By the coefficient of x or y

• By the vertex coordinates

Where is the vertex located in the given problem with x squared isolated?

• (3, 0)

• (0, 0)

• (0, 3)

• (-3, 0)

What is the equation of the directrix for the parabola with x squared isolated?

• x = 3

• y = -3

• x = -3

• y = 3

How is the focal width used in plotting a parabola?

• To plot additional points

• To determine the direction

• To find the vertex

• To calculate the value of p

What is the focal width of the parabola with x squared isolated?

• 6

• 8

• 12

• 10

In the new problem, what is the value of p?

• 2

• -2

• -3

• 3

Which direction does the parabola face in the new problem with y squared isolated?

• Up

• Down

• Left

• Right

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

• y = 2

• x = -2

• y = -2

• x = 2

How many units do you count up and down from the focus to use the focal width in the new problem?

• 5

• 4

• 3

• 2