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More translations

  1. Dec 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Let g(x) be the quadratic function:
    [tex] g(x) = (x - 1)^2 + 2 [/tex]

    A) Suppose h(x) is the result of g(x) undergoing a translation of 5 units to the right and 4 units up, and then a reflection over the y axis. find the coordinate of the vertex of h(x).

    B) A Transformation involving vertical and horizontal scale factors only

    [tex] h(x) \rightarrow ah(bx) [/tex]

    will bring the vertex of h(x) back to the vertex of g(x). Find the values of a and b (the rest of the function will *not* be the same as g(x)).

    2. Relevant equations

    [tex] y = af[b(x-h)] + k [/tex] [/tex]

    3. The attempt at a solution
    A) First i declared my translations:

    x -> x-5
    y -> y -4

    so far my function looks like this.

    y - 4 = (x-1-5)^2 + 2
    y = (x-6)^2 + 6

    now we have a reflection over the y axis.

    x -> -x, now my function looks like this. h(x) = (-x-6)^2 +6

    So the vertex must be where h(x) = 6, so i sub y in for 6.
    and solve for x

    6 = (-x-6)^2+6
    and i get x = -6, so the vertex would be (-6, 6), graphing calculator confirmed this.

    B) this is where i encountered issues.
    a and b equal the same as h(x) because its just a reflection, in
    y = ah(b(x-h))+k i declared b = -1, and a = 1, is this the right way to show my answer? but just to show how i would get the vertex back to g(x)'s vertex, i also stated the values for h and k, h = -5, k = -4. and stated that g(x) = h(-x+5) - 4, is this correct?
     
  2. jcsd
  3. Dec 27, 2008 #2

    olgranpappy

    User Avatar
    Homework Helper

    The above statement doesn't make sense (to me, at least)...

    Anyways, after cleaning up a little bit, you have:
    [tex]
    h(x)=(x+6)^2+6\;.
    [/tex]

    What is
    [tex]
    h(bx)
    [/tex]
    equal to?
     
  4. Dec 27, 2008 #3
    in the second part of the question (kind of jumps back to the top, sorry) it asks for the values of a and b, in order to translate h(x)'s vertex back to g(x)'s
    [tex]h(x) \rightarrow ah(bx)[/tex]
    where a is the vertical scale factor, and b is the horizontal scale factor.
     
  5. Dec 28, 2008 #4
    i haven't tried to solve it deeply but as much as i can see from here your way is fine. due to the fact that you have had 2 equations (y and its derivative) and 4 variables, you have had no choice but to set values for h and k in order to get the values of a and b.
     
  6. Dec 28, 2008 #5

    olgranpappy

    User Avatar
    Homework Helper

    Right... but, I'd like to know whether or not you can tell me:

    Given
    [tex]
    h(x)=(x+6)^2+6\;,
    [/tex]
    then
    what is
    [tex]
    h(bx)
    [/tex]
    equal to?
     
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