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Math Help - Find the Formula Associated with Each parabola

  1. #1
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    Find the Formula Associated with Each parabola

    the question is:

    part of a roller coaster is modeled by three parabola - some parts removed to give the diagram below.
    The first parabola from the left meets the second at co-ordinates (7, 14). using this information from the diagram how can i find the formula associated with each parabola and also workout their relevant domains? hint: think of the 3rd parabola is a translation of the first.


    Find the Formula Associated with Each parabola-parabola.jpeg
    could someone explain in steps if possible how the formulaes and the domains be obtained?
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  2. #2
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    Re: Find the Formula Associated with Each parabola

    To find the equation of a parabola passing through three given points, substitute the points' coordinates (x, y) into the equation y = ax^2 + bx + c. For each point (x, y) you'll get an equation on a, b and c. Then solve this system of three equations to find a, b, c.
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  3. #3
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    Re: Find the Formula Associated with Each parabola

    vertex form equation of a quadratic ...

    y = a(x-h)^2 + k

    where (h,k) is the vertex, and the value of the constant a can be determined by substituting any other point (x,y) that lies on the parabola.
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  4. #4
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    Re: Find the Formula Associated with Each parabola

    Quote Originally Posted by emakarov View Post
    To find the equation of a parabola passing through three given points, substitute the points' coordinates (x, y) into the equation y = ax^2 + bx + c. For each point (x, y) you'll get an equation on a, b and c. Then solve this system of three equations to find a, b, c.
    max(4.5, 20.25)-->y=ax^2+bx+c-->a(4.5)^2+b(4.5)+c
    -->20.25a+4.5b+c=14
    min(12, 1.5)-->y=ax^2+bx+c-->a(12)^2+b(12)+c
    -->144a+12b+c=1.5
    max(19.5, 20.25)-->=ax^2+bx+c-->a(19.5)^2+b(19.5)+
    -->380.25a+19.5b+c=20.25
    is this correct? what am i meant to do with the co-ordinates (7, 14)? and how do i proceed from this step to obtain not just the formula but ALSO the relevant domains?
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