Understanding Parabolas with Vertex at the Origin

This video tutorial explains how to find the equation of a parabola with its vertex at the origin, given the focus. It covers four cases: parabolas opening right, left, up, and down. The tutorial provides equations for each case and includes examples to illustrate the concepts. The focus and directrix are discussed in relation to the parabola's orientation.

What is the general form of the equation for a parabola that opens to the right or left?

• y = mx + c

• x^2 + y^2 = 1

• x^2 = 4py

• y^2 = 4px

If a parabola opens to the left, what can be said about the value of p?

• p is undefined

• p is zero

• p is positive

• p is negative

What is the general form of the equation for a parabola that opens up or down?

• x^2 + y^2 = 1

• y = mx + c

• y^2 = 4px

• x^2 = 4py

In the case of a parabola opening down, what is the relationship between the focus and the vertex?

• The focus is to the right of the vertex

• The focus is to the left of the vertex

• The focus is above the vertex

• The focus is below the vertex

For a parabola with a focus at (2.3, 0), what is the equation of the directrix?

• x = 2.3

• y = 2.3

• x = -2.3

• y = -2.3

What is the equation of a parabola with a vertex at the origin and a focus at (2.3, 0)?

• x^2 = 4.6y

• y^2 = 4.6x

• x^2 = 9.2y

• y^2 = 9.2x

For a parabola with a focus at (0, -3.54), what is the equation of the directrix?

• y = -3.54

• y = 3.54

• x = 3.54

• x = -3.54

What is the equation of a parabola with a vertex at the origin and a focus at (0, -3.54)?

• y^2 = 14.16x

• y^2 = -14.16x

• x^2 = 14.16y

• x^2 = -14.16y

If a parabola opens to the left, what is the form of its equation?

• x^2 = 4py

• y^2 = 4px

• x^2 + y^2 = 1

• y = mx + c

For a parabola with a focus at (0, 5.12), what is the equation of the directrix?

• x = -5.12

• y = -5.12

• y = 5.12

• x = 5.12