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linear function equation?

what is a and b if

y=m*x^2

x1=4

x2=12

x3=b

y1=a

y2=18

y3=72

I need to get the answers: a=2, b=24. 

how can get those answers can someone help me out, thank you.

2 Answers

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  • 2 months ago
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    Equation of the curve: y = mx²

    (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the point lying on the curve.

    Hence, (4, a), (12, 18) and (b, 72) lie on the curve.

    (12, 18) lies on the curve. Put x = 12 and y = 18 into the equation y = mx²:

    18 = m(12)²

    18 = 144m

    m = 18/144

    m = 1/8

    Equation of the curve: y = x²/8

    (4, a) lies on the curve. Put x = 4 and y = a into the equation y = x²/8:

    a = 4²/8

    a = 2

    (b, 72) lies on the curve. Put x = b and y = 72 into the equation y = x²/8:

    72 = b²/8

    b² = 576

    b = ±√576

    b = ±24

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  • 2 months ago

    The correct way of writing your problem is --

    Evaluate a  and  b if --

    y = m x^2

    Given that when -

    x = 4 , y = a ........... (1)

    x = 12, y  =  18........(2)

    x = b , y  =  72.........(3)

    Substitute these values in the given equation  y  =  m x^2  one by one .

    from (1) 

    => a  =  m (4)^2   =>   a  =  16 m .......   (A)

    from (2)    18  =  m (12)^2   =>   m  =  (18/144)  =  (1/8)

    m  =  (1/8)  ............. ( B)

    From (1) and (2)  a  = 16/8  =  2  .................. Answer

    Again, from (3) 

    72  =  (1/8) (b)^2

    =>  b^2  =  72*8  =>   b = 24   Answer

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