Parabola Properties and Equations

The video tutorial introduces graphing parabolas as conic sections, explaining the concepts of focus and directrix. It covers the basics of graphing parabolas with the vertex at the origin and provides examples of different orientations. Advanced graphing techniques are also discussed, including how to manipulate equations to isolate squared terms and determine the direction of the parabola based on the value of 'p'. The tutorial aims to equip students with the skills to graph parabolas accurately.

What shape is formed when a cone is sliced at an angle?

• Square

• Oval

• Triangle

• Circle

In a parabola, what is the point called that lies inside the curve?

• Apex

• Directrix

• Focus

• Vertex

What is the line called that is equidistant from the vertex as the focus?

• Axis

• Chord

• Tangent

• Directrix

What is the equation form for a parabola when x is squared?

• x^2 = 4py

• y^2 = 4px

• 4px

• 4py

If p is positive and x is squared, which direction does the parabola open?

• Down

• Right

• Left

• Up

What is the first step in graphing a parabola?

• Plot the directrix

• Find the vertex

• Find the value of p

• Determine the direction

In the equation x^2 = 12y, what is the value of p?

• 3

• 2

• 4

• 1

For the equation y^2 = -8x, which direction does the parabola open?

• Up

• Right

• Down

• Left

What is the focal width of a parabola if 4p equals 16?

• 8

• 4

• 16

• 12

In the example where 16x = y^2, what is the focus point?

• (4, 0)

• (0, -4)

• (-4, 0)

• (0, 4)