Results 1 to 4 of 4

Thread: Reciprocal functions

  1. #1
    Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    163
    Thanks
    1

    Question Reciprocal functions

    Hi,

    I hope someone can help.

    Remember that vertex form is y = a(x-h)^2+k

    I'm trying to understand why the function f(x) = 3x^2-4x-4 in vertex form is f(x) = (x-2/3)^2 - 16/9. Really what I'm wondering is why would k = -16/9 given that the vertex has a y-value of -5.3? I always was taught that the k value is the y-value for the vertex, so I'm wondering why this function has a k value which doesn't correspond to the vertex's y-value.

    Sincerely,
    Olivia
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    2,381
    Thanks
    902

    Re: Reciprocal functions

    $\begin{align*}f(x) & = 3x^2-4x-4 \\ & = 3\left(x^2-\dfrac{4}{3}x-\dfrac{4}{3}\right) \\ & = 3\left(x^2-\dfrac{4}{3}x + \dfrac{4}{9} - \dfrac{4}{9} - \dfrac{4}{3}\right) \\ & = 3\left(\left(x-\dfrac{2}{3}\right)^2 - \dfrac{16}{9}\right) \\ & = 3\left(x-\dfrac{2}{3}\right)^2 - \dfrac{48}{9}\end{align*}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2013
    From
    Colombia
    Posts
    1,744
    Thanks
    571

    Re: Reciprocal functions

    -\frac{48}9=-\frac{16}3=-5.333\ldots
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    163
    Thanks
    1

    Re: Reciprocal functions

    Thanks for your help!
    Last edited by otownsend; Apr 26th 2017 at 02:42 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rational and Reciprocal Functions
    Posted in the Algebra Forum
    Replies: 0
    Last Post: Oct 22nd 2011, 05:50 PM
  2. Replies: 2
    Last Post: Apr 9th 2010, 02:57 AM
  3. reciprocal
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: Feb 5th 2010, 09:11 AM
  4. reciprocal functions question
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Dec 30th 2009, 08:18 AM
  5. Derivative of reciprocal functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jun 4th 2008, 02:21 PM

Search Tags


/mathhelpforum @mathhelpforum