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# Finding explicit formula

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I have a curved graph with only two coordinates... (-2,5) and (2,1) How do I determine the explicit formula for this curve?

Guest May 29, 2017
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With only two coordinates  given, there could be many possibilities......

One possibilty  can be found by solving the system for a and b  to generate a polynomial in the form  y = ax^2  + bx

a(-2)^2  + b(-2)   = 5

a(2)^2  + b(2)  =    1       simplify

4a  - 2b   = 5

4a  +  2b  = 1         add the equations

8a   = 6      divide by 8 on both sides

a   =  6/8  =  3/4

And  using  4a - 2b =  5    to solve for b, we have

4(3/4) - 2b  =  5

3 -  2b  =  5

-2b  =   2     divide through by -2

b  = -1

So.......a possible function is :

y =  (3/4)x^2  - 1x

CPhill  May 29, 2017
edited by CPhill  May 29, 2017

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