1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper

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

    Anyways, after cleaning up a little bit, you have:

    What is
    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


    User Avatar
    Homework Helper

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

    what is
    equal to?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook