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Math Help - determine constants

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    Senior Member euclid2's Avatar
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    determine constants

    Determine values of a,b,c such that the graph y=ax^2+bx+c has a relative maximum at (3,12) and crosses the y axis at (0,1)
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    Quote Originally Posted by euclid2 View Post
    Determine values of a,b,c such that the graph y=ax^2+bx+c has a relative maximum at (3,12) and crosses the y axis at (0,1)
    first, you have two points on the curve given to you ...

    (0,1) ... 1 = a(0^2) + b(0) + c ... now you know c = 1

    (3,12) ... 12 = a(3^2) + b(3) + 1

    this gives you the equation 9a + 3b = 12 , or simplified, 3a + b = 4

    now you need another equation ... relative extrema occur at critical values; in this case where y' = 0.

    y = ax^2 + bx + 1

    y' = 2ax + b

    2ax + b = 0 at x = 3 ...

    6a + b = 0

    there is your second equation in terms of a and b ... solve the system.
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