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Math Help - Parabola: finding the a and q values

  1. #1
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    Parabola: finding the a and q values

    I need help with finding the a and q values if the defining equation f is f(x)= ax^2 + q

    with the x and y values being (-3;6) and (3;6)
    x y x y

    How would u go about solving this equation
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  2. #2
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    Quote Originally Posted by Mixxie16 View Post
    I need help with finding the a and q values if the defining equation f is f(x)= ax^2 + q

    with the x and y values being (-3;6) and (3;6)
    x y x y

    How would u go about solving this equation
    Notice what happens when x is 3 or -3

    3^2=9.

    But we know that the y value is supposed to equal 6, not 9. So the q value should subtract 9-6=3.

    y=x^2-3 suits the two ordered pairs you were given.
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  3. #3
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    Quote Originally Posted by Mixxie16 View Post
    I need help with finding the a and q values if the defining equation f is f(x)= ax^2 + q

    with the x and y values being (-3;6) and (3;6)
    x y x y

    How would u go about solving this equation
    Hi Mixxie,

    if a=1, then q=-3

    You need 2 clues to find "a" and "q".

    The two pieces of information you are given are unfortunately
    not giving two simultaneous equations as they are both

    9a+q=6

    since (-3)^2=3^2

    The graph of the function is parabolic, the axis of symmetry is the y-axis.

    f(0)=q

    There are an infinite number of solutions until another clue is given.

    a=2,\ 2(9)+q=6,\ q=-12

    a=3,\ 3(9)+q=6,\ q=-21

    etc
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