Understanding Parabolas

The video tutorial explains how to graph parabolas by finding the value of p, determining the direction the parabola faces, and identifying key components such as the vertex, focus, and directrix. It covers both x-squared and y-squared equations, demonstrating how to plot these parabolas on a graph. The tutorial also explains how to calculate and use the focal width to complete the graphing process.

What is the first step in graphing a parabola?

• Find the vertex

• Determine the direction it faces

• Find the value of p

• Plot the directrix

How do you determine the direction a parabola faces?

• By the sign of p

• By the focal width

• By the vertex coordinates

• By the coefficient of x or y

Where is the vertex located in the given problems?

• (0, 0)

• (1, 1)

• (-1, -1)

• (2, 2)

What is the role of the directrix in a parabola?

• It is the axis of symmetry

• It is a reference line

• It is a point on the parabola

• It is the focal point

How is the focal width of a parabola determined?

• By the vertex

• By the directrix

• By the focus

• By the value of 4p

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

• 12

• 8

• 14

• 10

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

• -2

• 2

• -3

• 3

Which direction does the parabola with y squared open?

• Up

• Down

• Right

• Left

What is the equation of the directrix for the parabola with y squared?

• y = 2

• y = -2

• x = 2

• x = -2

How many units do you count from the focus to plot additional points for the parabola with y squared?

• 6

• 4

• 8

• 2