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March 26, 2017

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The curve with equation y = ax^2 + bx + c passes through the points P(2,6) abd Q(3,16), and has a gradient of 7 at the point P. Find the values of the constants a,b and c.

Thanks!

  • Math: Integration - ,

    These conditions must be satisfied:
    6 = a*2^2 + b*2 + c = 4a + 2b + c
    16 = 9a + 3b + c
    dy/dx @ P = 2a*2 + b = 4a + b = 7

    Solve those three equations in 3 unknowns. It does not require integral calculus.
    4a + 2b + c = 6
    4a + b = 7
    Combine these two to get b + c = -1

    36a + 12 b + 4c = 64
    36a + 18 b + 9c = 54
    Combine the last 2 to get
    6b + 5c = -10
    Now you have two equations in two unknowns. Use substitution to eliminate one of the variables.
    6b + 5(-1 -b) = -10
    b = -5
    4a = 7-b = 12 ; a = 3
    5c = -10 -6b = -10 + 30 = 20
    c = 4
    y = 3x^2 -5x + 4

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