Simple Graph Problem.

Posted on 2005-04-18
Last Modified: 2006-11-18

Let's say that I have a linear equation, for example:

   y = 0.25x - 4

Now, at what value of 'x' should I start and end? Do I only need to do 2 points and just draw a long straight line throught both points (I'm aware that if this is the case, it wouldn't work for quadratic graphs)??

It's the same with Quadratic graphs, how to work out from an equation at what values of 'x' I need to start and end with?

Question by:InteractiveMind
    LVL 33

    Assisted Solution

    Line are infinite.  You can plug in any value of x and get a value for y.  If you're trying to draw a graph, then you only need 2 points - choose values that are convenient to draw.  It's probably easiest if you choose values for x that are multiples of 4, since you'll get whole numbers for y.
    LVL 33

    Expert Comment

    Quadratics are also infinite.  However, the interesting bits are usually where the curve changes directions, so you'll need to find the minimum or maximum value.

    If your quadratic is of the form
    y = ax² + bx + c
    Then we can take the the derivative, set it equal to 0, and find that the minimum or maximum has the x value
    x = -b / (2a)

    You'll also want to plug in a few values for x on either side of this number to define the shape of the curve.
    LVL 18

    Expert Comment

    You need 2 points and a ruler for a straight line (y = mx + c)

    You need 3 points and a variable parabola tool (VPT) for plotting a quadratic (y = ax^2 + bx + c).
    As VPTs are quite hard to come by, your better off drawing a lot of points and joining the dots.

    LVL 26

    Expert Comment

    The "best" points to use for plotting a line are probably the x- and y-intercepts:

    Set x = 0    ==>  y = 4

    Set y = 0   ==>  0.25x - 4 = 0  ==>  x = 1
    LVL 26

    Expert Comment


      Set y = 0   ==>  0.25x - 4 = 0  ==>  x = 16

    LVL 18

    Expert Comment

    For a quadratic (y = ax^2 + bx + c) you can work out where/if it crosses the x axis from
    x= -b +/- sqrt(b^2 - 4ac)/2a
    LVL 3

    Accepted Solution


    I think what you are asking might relate to exam-taking (judging from another post of yours).  I think you might be asking what to do, given your time constraints, if a question on an exam says, Plot y = 0.25x - 4, or Plot y = ax² + bx + c.

    First, for the line:
    As d-glitch said, the x and y-intercepts are the easiest points to use in general.  Label the points or the relevant cross-hatches on the axes.

    In a rare case, the line will cross an axis with a large value and you won't want to draw so many cross-hatches.  Then choose some other convenient value.

    As you said, sketch a line going through the two points.  Make sure it extends slightly beyond the points, and put arrows on both ends.

    In exams, it's always a good idea to do some sort of independent check.  In this case, you could find a third point and make sure it's on the line you drew.  You could also calculate the slope and make sure that matches.

    I don't know anything about the exam you will take, but often exams that cover this material present an equation for a line in several other forms, besides the form you mentioned in your question.  It would be good to be familiar with the other standard forms.  I hope you have a book with plenty of worked examples.

    For the parabola:
    As snoyes jw said, plot the extremum (i.e. the minimum or maximum).  Personally, what I would do next is see if the parabola is opening up or down.  There are a couple ways you could do this.  One is to choose a value of x near the extremum and see if it gives you a y-value that's bigger or smaller.

    That's what I do when I'm plotting a parabola.  But I have a feeling they may want to see the focus and the directrix.  I have not done those in years.  I found a link that explains how:
    (You can skip directly to "Graphing Method".)
    However, you might be able to find some other site you like better.  Ideally, you should be working with a book that matches up pretty well with the exam you'll be taking.


    Featured Post

    6 Surprising Benefits of Threat Intelligence

    All sorts of threat intelligence is available on the web. Intelligence you can learn from, and use to anticipate and prepare for future attacks.

    Join & Write a Comment

    We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
    Article by: Nicole
    This is a research brief on the potential colonization of humans on Mars.
    Internet Business Fax to Email Made Easy - With eFax Corporate (, you'll receive a dedicated online fax number, which is used the same way as a typical analog fax number. You'll receive secure faxes in your email, fr…
    Polish reports in Access so they look terrific. Take yourself to another level. Equations, Back Color, Alternate Back Color. Write easy VBA Code. Tighten space to use less pages. Launch report from a menu, considering criteria only when it is filled…

    728 members asked questions and received personalized solutions in the past 7 days.

    Join the community of 500,000 technology professionals and ask your questions.

    Join & Ask a Question

    Need Help in Real-Time?

    Connect with top rated Experts

    19 Experts available now in Live!

    Get 1:1 Help Now