Equations of Parabolas

​Equations of Parabolas:

Focus, Directrix, & Equidistance​

Multiple Choice

A directrix is...

• A type of wizard from Harry Potter

• fixed line of the parabola, perpendicular to the AOS

• another name for the Axis of Symmetry

• fixed line of the parabola, parallel to the AOS

​Parabola -the set of all points in a plane that are the same distance from a fixed line and a fixed point.

Focus - the fixed point of a parabola

Directrix - the fixed line of the parabola, perpendicular to the AOS

Focal Length - the distance between the vertex and the focus

Wait, what do those words mean???

Multiple Choice

The focus is always inside the parabola.

• true
• false

What does this mean?

Multiple Choice

You can pick any point on the parabola, and it will always be the same distance from the focus and the directrix.

• True

• False

Multiple Choice

What is the green dashed line called?

• roots or x-intercepts
• parabola
• axis of symmetry
• line of dashes

Breaking it down

Multiple Choice

All parabolas with a vertical directrix open the left or right.

• true
• false

Concavity describes the orientation of the curvature of the parabola. The vertex of a parabola is the point on the axis of symmetry which is exactly midway between the focus and the directrix. It is also the point where the parabola changes direction.

​

Concavity

Multiple Choice

The vertex is halfway between the focus and directrix.

• true
• false

Multiple Choice

What is an equation of a parabola with a vertex at the origin and a focus of (0,2)?

• $$y=-\frac{1}{8}x^2$$  

• $$y=\left(x-8\right)^2$$  

• $$y=8x^2$$  

• $$y=\frac{1}{8}x^2$$  

Multiple Choice

What is an equation of a parabola with a vertex at the origin and a focus of (0,-1.5)?

• $$y=-\frac{1}{6}x^2$$  

• $$y=x^2+1.5$$  

• $$y=6x^2$$  

• $$y=-1.5x^2$$  

Multiple Choice

What are the vertex, focus, and directrix of a parabola with equation $$y=-\frac{1}{12}x^2$$  ?

• vertex (0,1)

  focus (0,-6)

  directrix y=-3

• vertex (1,1)

  focus (-3,1)

  directrix y=12

• vertex (0,0)

  focus (0,-3)

  directrix y=3

• vertex (12,0)

  focus (0,-6)

  directrix y=1/12

Multiple Choice

Given the graph, what is the axis of symmetry of this parabola?

• $$x=-1$$

• $$x=-4$$

• $$y=-1$$

• $$y=-4$$

Multiple Choice

What is an equation of a parabola with a focus (2,3) and a directrix x=-4?

• $$x=\frac{1}{12}\left(y-3\right)^2-1$$  

• $$y=\frac{1}{12}x^2-4$$  

• $$x=-4\left(y-3\right)^2$$  

• $$y=4\left(x-2\right)^2+1$$  

Multiple Choice

What is an equation of a parabola with focus (0,7) and directrix y=-1?

• $$x=16y^2-3$$  

• $$y=\frac{1}{16}x^2+3$$  

• $$x=7y^2-1$$  

• $$y=7x^2-1$$