Results 1 to 4 of 4

Thread: I need your help bruddas! ASAP! STAT! NOW!

  1. #1
    Newbie
    Joined
    Jun 2007
    Posts
    22

    Angry I need your help bruddas! ASAP! STAT! NOW!

    For the parabola whose range is y <_ 3 , whose x-coordinate of the turning point -4 and whose y-intercept is y= - 2 1/3

    Find the Y coordinate of the turning point.
    The equation of the parabola
    The coordinates of the x-intercepts.

    -----------------------------------------------------------------

    The parabola has a turning point at (Z, -8); it intersects the y-axis at y=10 and one of the x-intercepts is x=5.

    Find the value of Z.
    Find the equation of the parabola.

    -----------------------------------------------------------------

    The graph of $\displaystyle y = a(h - x)^3 + k$ cuts the x-axis at x = - 4 and the y axis and y= 28. It has a dilation of 1.

    Find the position of the SPOI.
    -----------------------------------------------------------------

    Thanks
    Help would be appreciate.

    Cheers
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Quote Originally Posted by mibamars View Post
    For the parabola whose range is y <_ 3 , whose x-coordinate of the turning point -4 and whose y-intercept is y= - 2 1/3
    What have you done?

    The Range restriction is in 'y', so this must open up or down. None of that left or right stuff.

    You then have y - k = a(x-h)^2

    You are given k = 3 and a < 0 and h = -4

    y - 3 = a(x+4)^2

    Substitute x = 0 and find the value for 'a' that gives y = -7/3.

    Let's see what you get.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Thanks
    1
    Awards
    1
    Quote Originally Posted by mibamars View Post
    For the parabola whose range is y <_ 3 , whose x-coordinate of the turning point -4 and whose y-intercept is y= - 2 1/3

    Find the Y coordinate of the turning point.
    The equation of the parabola
    The coordinates of the x-intercepts.
    Try to post one question at a time. It leads us to believe you just want questions answered for homework when you post so many at once within one thread.

    I assume turning point is where the graph turns, hence where a max or min is at. This is also known as a critical point. The graph is a parabola, and it has a maximum value at $\displaystyle y=3$ thanks to the given range. Therefore, that maximum must be the critical point at $\displaystyle x=-4$. The coordinates of the critical point are then (-4, 3).

    The parabola takes on this equation: $\displaystyle y=a(x+c)^2+b$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, mibamars!

    Here's the first one . . .


    For the parabola whose range is $\displaystyle y \leq 3$,
    whose x-coordinate of the turning point is -4,
    and whose y-intercept is $\displaystyle -\frac{7}{3}$

    Find:
    (1) the y-coordinate of the turning point.
    (2) the equation of the parabola
    (3) the coordinates of the x-intercepts.

    The general equation of a parabola is: .$\displaystyle y \;=\;ax^2+bx + c$

    Make a sketch . . .
    Code:
                          |
               (-4,3)     |
                  *       |
               *     *    |
             *         *  |
            *           * |
          - - - - - - - - + - - - - -
           *             *|
                          |
                          |
          *               *
                          |
    Since $\displaystyle \left(0,\,-\frac{7}{3}\right)$ is on the parabola: .$\displaystyle -\frac{7}{3} \:=\:a\!\cdot\!0^2 + b\!\cdot\!0 + c\quad\Rightarrow\quad \boxed{c \:=\:-\frac{7}{3}}$

    The equation (so far) is: .$\displaystyle y \;=\;ax^2 + bx - \frac{7}{3}$


    Since the range (values of y) is < 3,
    . . and the x-coordinate of the turning point is -4,
    . . clearly the vertex is (-4,3).

    $\displaystyle {\color{red}\text{(1) The }y\text{-coordinate of the turning point is }3.}$



    The x-coordinate of the vertex is given by: .$\displaystyle \frac{-b}{2a}$
    . . So we have: .$\displaystyle \frac{-b}{2a} \:=\:-4\quad\Rightarrow\quad 8a - b \:=\:0$ . [1]

    Since (-4,3) is on the parabola: .$\displaystyle 3 \:=\:a(\text{-}4)^2 + b(\text{-}4) - \frac{7}{3}$
    . . which simplifies to: .$\displaystyle 16a - 4b \:=\:\frac{16}{3}\quad\Rightarrow\quad 4a - b \:=\:\frac{4}{3}$ . [2]

    Subtract [2] from [1]: .$\displaystyle 4a \:=\:-\frac{4}{3}\quad\Rightarrow\quad\boxed{ a \:=\:-\frac{1}{3}}$

    Substitute into [1]: .$\displaystyle 8\left(\text{-}\frac{1}{3}\right) - b \:=\:0\quad\Rightarrow\quad\boxed{ b \:=\:-\frac{8}{3}}$

    $\displaystyle {\color{red}\text{(2) The equation of the parabola is: }\:y \;=\;-\frac{1}{3}x^2 - \frac{8}{3}x - \frac{7}{3}}$



    For the x-intercepts: .$\displaystyle -\frac{1}{3}x^2 - \frac{8}{3}x - \frac{7}{3} \;=\;0$

    Multiply by -3: .$\displaystyle x^2 + 8x + 7 \:=\:0$

    . . Factor:.$\displaystyle (x+7)(x+1) \:=\:0\quad\Rightarrow\quad x \:=\:-7,-1$


    $\displaystyle {\color{red}\text{(3) The }x\text{-intercepts are: }\:(-7,0), (-1,0)}$

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. density for order stat, sufficient stat, MLE question
    Posted in the Advanced Statistics Forum
    Replies: 13
    Last Post: Mar 14th 2011, 12:50 AM
  2. t-stat
    Posted in the Statistics Forum
    Replies: 0
    Last Post: Dec 10th 2010, 06:44 PM
  3. AP Stat help!
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Nov 29th 2009, 01:33 PM
  4. stat Q
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Mar 1st 2009, 09:00 AM
  5. Please Help with this Stat Q
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: Mar 27th 2008, 04:28 PM

Search Tags


/mathhelpforum @mathhelpforum