Graphing a Parabola

Date: Mon, 12 Dec 94 02:08:02 EST
From: Anonymous
Subject: Parabola

How do I graph a parabola (without a calculator)?

Date: Thu, 15 Dec 1994 19:50:42 -0500 (EST)
From: Dr. Sydney
Subject: Re: Parabola

Hi there,

Hello!  Thanks for writing to us.  I guess the easiest way to graph
a parabola is first to figure out the vertex and the direction the parabola
will open up.  Then after plotting a few points you should have a pretty
good sense of what the graph looks like.  

A parabola with vertex (h,k) and axis parallel to the coordinate axes can 
be represented by:

  c(y-k) = (x - h)^2  when its axis is vertical

or

  c(x-h) = (y-k)^2    when its axis is horizontal

So, if you are given the equation for a parabola you first want to put it
into one of the forms above.  Say for example you are given the equation: 

        x^2 - 6x - 6y +3 = 0

Then, you would put it into the above form by completing the square 
to get:

        (x-3)^2 = 6(y + 1)

Now, since it is in the form above, we can say lots about the parabola.  
In our example, h = 3 and k = (-1), while c = 6. 

That means the vertex of the parabola is at the point, (3, -1).  Because c
is positive, the parabola opens in the positive direction.  

Which kind of parabola is it, though?  The kind that looks kind of like a 
u or the kind that is a sideways u?  If you have a y^2 in your equation, 
the parabola will look like a sideways u.  If you have an x^2 in your 
equation, the parabola will look like a u or an upside down u.

So, in our example, we have a parabola that has an x^2 in it. Because it
opens in the positive direction, it will look like a u.  

Now, you can plot points.  First plot the vertex ((3, -1) in our example).
Then, plot maybe 2 or 3 more points...you'll get enough of a sense for 
the parabola after that.  

I hope this helps.  Write back if you have any more questions.

--Sydney