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Transforming quadratic functions

  1. Jul 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Sketch the graph of y=x^2 and graph y=1/2(x+4)^2 -5

    2. Relevant equations

    3. The attempt at a solution

    So, This is the method I use for vertical compression/expansion

    Step pattern of a parabola at y=x^2 is 1,3,5

    Start at vertex, go out by one, go up by 1 and plot the point. From that point, you go out by 1 go up by 3, plot the point. then go out by one, go up by 5 and plot the point.. use symmetry to get the other side and that gives you y=x^2 of a porabola.

    If you have something like y=4(x-2) +4

    then the vertex is (2,4) , and since there is a vertical stretch you multiply the step pattern of, 1,3,5 by 4 , giving you, 4 ,12, 20, ... effectively... Start at the vertex of 2,2 . and go out by 1 and up by 4, plot the point, then go out by one up by 12, plot the point. and so forth, that is what ive learned as the step pattern for a parabola. when you have vertica lstretch you multiply by 4.

    Why doesnt this work now? Usually when you have a graph like 1/2(x-4)^2 +5
    You go to the left 4 units, up 5 units, then multiply the step patern of 1,3,5 by 0.5. But for some reason that doesnt work. So how the hell do you do a vertical stretch on the parabola?
  2. jcsd
  3. Jul 17, 2011 #2


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    Homework Helper

    for the (x-4)2 part, you'd need to shift the graph of x2 four (4) units to the right. Then you'd need to stretch (x-4)2 by the factor of ½ and then the vertical translation.

    I've never really learned transformation graphs as 1,3,5 so I am not sure if I am telling you something you already know.
  4. Jul 17, 2011 #3


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    Earlier, you wrote y = 1/2(x + 4)2 - 5. Which one is it? I'm going to assume that you mean
    y = 1/2(x - 4)2 + 5

    It does work. But you have to go the right 4 units and up 5 units to plot the vertex. So if you plot the points
    (4, __)
    (5, __)
    (6, __)
    (7, __)
    (I'll let you fill in the blanks), then you'll see that the step pattern (multiplied by 1/2) is applied.

    Don't forget that regarding transformations, if we start with y = f(x), then
    y = f(x - c) is a transformation to the right by c units, and
    y = f(x + c) is a transformation to the left by c units.
    I've seen a lot of students get those mixed up.
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