Graph Parabolas: Quadratic Equations Explained

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Discussion Overview

The discussion revolves around the methods for graphing parabolas and quadratic equations, including various approaches and formulas. Participants explore both theoretical and practical aspects of graphing, including the use of calculators and plotting points.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest using calculators or plotting points to graph parabolas.
  • One participant outlines the standard forms of parabolas and explains how to identify the vertex, focus, and directrix.
  • Another participant describes how to determine the direction in which a parabola opens based on the value of 'a' in the equations.
  • There are mentions of using conic equations for parabolas and the importance of finding intercepts for graphing.
  • One participant expresses confusion over a proposed equation with multiple variables, leading to clarification about whether it was a quadratic or linear equation.
  • Another participant acknowledges the need for three points to accurately graph a parabola, correcting their earlier statement about needing fewer points.
  • There is a suggestion that if a third variable is present, the equation may represent a plane rather than a parabola.

Areas of Agreement / Disagreement

Participants generally agree on the methods for graphing parabolas, such as the need for three points, but there are varying opinions on the best approach and some confusion regarding specific equations. The discussion remains unresolved regarding the handling of equations with multiple variables.

Contextual Notes

Some participants reference specific forms and properties of parabolas without fully resolving the implications of different variable configurations. There is also a lack of consensus on the best methods for graphing when additional variables are introduced.

Imparcticle
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How do I graph parabolas/quadratic equations?
 
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Either use a calculator, or just plot points.

cookiemonster
 
Ick, your making me remember how to graph stuff without calc?

Ill start off by assuming you mean a straight forward parabola without a rotation or anything.


First you need to put the parobala in the form:

Y = a(x – h)^2 + k
Or
X = a(y – h)^2 + h

Where a=1/4p

The position of your vertex (the extreme point) is (h,k)

The focus is (h, k + p) and the directrix line is y = k – p

The other 2nd degree quadratics have similar geometric formulas. Maybe you can show us what you need to graph…
 
Last edited:
Oops forgot to tell you how to find which way it opens.

For
X = a(y – h)^2 + h
If a < 0 then it opens to the left
If a > 0 then it opens to the right

For
Y = a(x – h)^2 + k
If a < 0 then it opens down
If a > 0 then it opens up
 
cookiemonster said:
Either use a calculator, or just plot points.

cookiemonster

I think it will be easier to just plug in points and go from there.
 
Chrono said:
I think it will be easier to just plug in points and go from there.
to make a parabola graph you only need three points, if less then it's not kosher.
 
Aside from the simple y=(x-a)^2+b formulas, there's also conics equations for parabolas:
4py=x^2, where p is the distance to your focus or directrix. (the focus is an arbirtrary point, and the directrix is a line whos equation is y=-d, where d is the distance from y=0 to focus).
As far as graphing, either get a simple table of values, or get three points: two X intercepts and one Y intercept. To get the X intercepts, simply substitute 0 into y so that your equation looks like 0 = (x-a)^2 + b, which shouldn't be too hard to solve. For the Y intercept, do the same, but substitute x as 0, so that you end up with y=(0-a)^2+b , which should be pretty easy to get as well.
after you're done that, plot your points, and draw a curve through them.
 
how about graphing something like y=3x+5b+3?
 
:eek: You have got more variables in there than I am am comfortable to deal with!
 
  • #10
did u mean y = 3x^2 + 5x + 3?

if u didnt:
thats just a simple linear equation (im assuming that b is a constant - if its a variable u can't graph it) that has a y-intercept of 5b + 3 and a slope of 3..
 
  • #11
loop quantum gravity said:
to make a parabola graph you only need three points, if less then it's not kosher.

You're right, of course. For some reason I was thinking of a line when I said what I did.
 
  • #12
Parth Dave said:
did u mean y = 3x^2 + 5x + 3?

Yes. (my bad) :rolleyes:
 
  • #13
for that kind i just use a graphics calculator, i think if you want to look at that and draw it you have to play with the equation a bit till its easier. i 4got the format i used last year for this type of thing.
 
  • #14
If b is a third variable (call it z, for familiarity), then I believe you are looking at the equation of a plane.
 

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