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
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