Results 1 to 3 of 3

Math Help - How to find the equation of a Parabola

  1. #1
    Junior Member 22upon7's Avatar
    Joined
    Nov 2008
    Posts
    60

    How to find the equation of a Parabola

    Hi,

    Could someone explain step-by-step, how to work through this type of sums:

    "Find the equation of the quadratic which passes through the points with coordinates:

    (-2,-1), (1,2), (3,-16)"

    I substituted the values in to the equation ax^2+bx+c

    -1=4a-2b+c
     2 =a+b+c
    -16=9a+3b+c

    I'm not sure how you work out the simultaneous equations though, Any help would be much appreciated,

    Thanks,

    Dru
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, 22upon7!

    You did the hard part . . . and you forgot your algrbra?


    Find the equation of the parabola which passes through the points
    . . with coordinates: .(-2,-1), (1,2), (3,-16)

    I substituted the values in to the equation y \:=\:ax^2+bx+c

    -1=4a-2b+c
     2 =a+b+c
    -16=9a+3b+c

    We have: . \begin{array}{cccc}a + b + c &=& 2 & {\color{blue}[1]} \\ 4a - 2b + c &=& \text{-}1 & {\color{blue}[2]}\\ 9a + 3b + c &=& \text{-}16 & {\color{blue}[3]} \end{array}


    Subtract {\color{blue}[2] - [1]}\!:\;\;3a - 3b \:=\:\text{-}3 \;\;\quad\Rightarrow\quad a - b \:=\:\text{-}1\;\;{\color{blue}[4]}

    Subtract {\color{blue}[3] - [2]}\!:\;\;5a + 5b \:=\:\text{-}15 \quad\Rightarrow\quad a + b \:=\:\text{-}3\;\;{\color{blue}[5]}


    Add {\color{blue}[4] + [5]}\!:\;\;2a \:=\:-4 \quad\Rightarrow\quad\boxed{ a \:=\:-2}

    Substitute into {\color{blue}[5]}\!:\;\;-2 + b \:=\:-3 \quad\Rightarrow\quad \boxed{b\:=\:-1}

    Substitute into {\color{blue}[1]}\!:\;\;-2 -1 + c \:=\:2 \quad\Rightarrow\quad\boxed{ c \:=\:5}


    Therefore: . y \;=\;-2x^2 - x + 5

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member 22upon7's Avatar
    Joined
    Nov 2008
    Posts
    60
    Quote Originally Posted by Soroban View Post
    Hello, 22upon7!

    You did the hard part . . . and you forgot your algrbra?



    We have: . \begin{array}{cccc}a + b + c &=& 2 & {\color{blue}[1]} \\ 4a - 2b + c &=& \text{-}1 & {\color{blue}[2]}\\ 9a + 3b + c &=& \text{-}16 & {\color{blue}[3]} \end{array}


    Subtract {\color{blue}[2] - [1]}\!:\;\;3a - 3b \:=\:\text{-}3 \;\;\quad\Rightarrow\quad a - b \:=\:\text{-}1\;\;{\color{blue}[4]}

    Subtract {\color{blue}[3] - [2]}\!:\;\;5a + 5b \:=\:\text{-}15 \quad\Rightarrow\quad a + b \:=\:\text{-}3\;\;{\color{blue}[5]}


    Add {\color{blue}[4] + [5]}\!:\;\;2a \:=\:-4 \quad\Rightarrow\quad\boxed{ a \:=\:-2}

    Substitute into {\color{blue}[5]}\!:\;\;-2 + b \:=\:-3 \quad\Rightarrow\quad \boxed{b\:=\:-1}

    Substitute into {\color{blue}[1]}\!:\;\;-2 -1 + c \:=\:2 \quad\Rightarrow\quad\boxed{ c \:=\:5}


    Therefore: . y \;=\;-2x^2 - x + 5

    Thankyou!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: March 22nd 2011, 05:57 PM
  2. Find the equation for the parabola...
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 8th 2010, 08:01 PM
  3. Parabola - find the equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 22nd 2010, 11:44 PM
  4. Find Parabola Equation
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 23rd 2008, 10:38 PM
  5. Find parabola equation
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 14th 2008, 03:55 AM

Search Tags


/mathhelpforum @mathhelpforum