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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

#1**+1 **

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