Math

Welcome to the wonderful world of Parabolas!!!!! Aren't they great!!!!
Using this page you will learn all about Parabolas and answer questions about them too.


Examples
The basic parabola formula is y=x2. This looks like

To make a horizontal translation we add an "b" coordinate.
Example
y=x2+2x would look like

To make a vertical translation we add a "c" coordinate.
Example
y=x2+2 would look like

Here is an example of what y=x2+2x+2 would look like.
This example has both a vertical and horizontal translation.

This is what y=-x2 looks like.
This is a reflection in the x axis.

To get a horizontal stretch
2y=x2
or
y=2x2

Here is an example with a horizontal stretch, a horizontal translation and a vertical translation.
2y=x2+2x+2

These two have horizontal and vertical translations, a horizontal stretch and a reflection.
-2y=x2+2x+2
y=-2x2-2x+2


OK you've seen enough examples. Now see how much you learned. Take this test and see how you do.

1. What does a horizontal translation do to the graph?

A horizontal translation moves the graph ___________ .

Up?
Down?
  Left or right?
  To a different website?

2. What does a vertical translation do to a graph?

A vertical translation moves the graph ___________ .

Left?
Up?
  Down?
  Up or down?

3. What happens when we reflect a graph in the x-axis?

When we add a reflection ___________ .

it flips the graph over (upside down)
it moves the graph up or down
  it makes it look like a mirror
  it moves it 2 spaces to the right

4. What is the basic parabolic equation?

The basic equation for a parabola is ___________ .

x=y2?
y=x?
  y=x2
  y=mx+b

5. What does a horizontal stretch do to a graph ?

A horizontal stretch ___________ .

moves it up or down?
moves it left or right?
  flips the graph
  stretches the graph or shrinks it?

6. What would a graph with the coordinates y=2x2+3x-1 look like?

It would look like ___________ .



 
 

6. What would a graph with the coordinates 2y=-x2-x look like?

It would look like ___________ .



 
 

7. What would a graph with the coordinates y=x2+2x look like?

It would look like ___________ .



 
 

8. What would a graph with the coordinates 2y=x2+3 look like?

It would look like ___________ .



 
 

9. The equation y=-x2 would have what kind of transformation?

It would have a ___________ .

A horizontal translation?
A vertical stretch?
  A reflection in the x axis?
  A horizontal stretch?

10. To move a graph vertically by two units the equation would be?

The equation would be ___________ .

2y=x2
y=x2+2
  y=x2+2x
  y=2x2+4

Alright you've completed the test!!! To learn more about parabolas go to Math.com or Graphmatica.com