Understanding Parabolas with Vertex at the Origin

This video tutorial explains how to determine the equation of a parabola with its vertex at the origin, given the directrix. It covers four examples, each illustrating a different orientation of the parabola based on the position of the directrix. The tutorial provides step-by-step instructions on plotting the vertex and directrix, identifying the focus, and deriving the equation of the parabola in standard form.

What is the form of the equation for a parabola that opens downwards with its vertex at the origin?

• y^2 = 4px

• x^2 = -4py

• y^2 = -4px

• x^2 = 4py

If the directrix of a parabola is a horizontal line above the vertex, where is the focus located?

• To the right of the vertex

• To the left of the vertex

• Below the vertex

• Above the vertex

For a parabola with a vertical directrix to the right of the vertex, in which direction does it open?

• To the right

• To the left

• Downwards

• Upwards

What is the equation form for a parabola that opens to the left with its vertex at the origin?

• y^2 = -4px

• x^2 = 4py

• y^2 = 4px

• x^2 = -4py

If the directrix is to the left of the vertex, where is the focus located?

• Below the vertex

• To the left of the vertex

• To the right of the vertex

• Above the vertex

What is the form of the equation for a parabola that opens to the right with its vertex at the origin?

• y^2 = -4px

• x^2 = -4py

• x^2 = 4py

• y^2 = 4px

For a parabola with a horizontal directrix below the vertex, in which direction does it open?

• To the right

• To the left

• Downwards

• Upwards

What is the equation form for a parabola that opens upwards with its vertex at the origin?

• x^2 = 4py

• y^2 = 4px

• y^2 = -4px

• x^2 = -4py

If the directrix is below the vertex, where is the focus located?

• Above the vertex

• Below the vertex

• To the left of the vertex

• To the right of the vertex

What is the value of 'p' if the directrix is 8/3 units below the vertex?

• 8/3

• -8/3

• 5/3

• -5/3