SOLUTION: hard question Find the quadratic equation that fits the following set of data points {(-2,18),(-5,87),(4,42)} Write the equation in the stanrd form, y=ax^2+bx+c. Thank you.

{(-2,18),(-5,87),(4,42)}

The first point is (x,y) = (-2,18).
So substitute -2 for x and 18 for y in

          y = ax² + bx + c

and get

         18 = a(-2)² + b(-2) + c
         18 = a(4) - 2b + c
         18 = 4a - 2b + c

Switch the left side with the right side:

4a - 2b + c = 18

That's one equation.

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The second point is (x,y) = (-5,87).
So substitute -5 for x and 87 for y in

          y = ax² + bx + c

and get

         87 = a(-5)² + b(-5) + c
         87 = a(25) - 5b + c
         87 = 25a - 5b + c

Switch the left side with the right side:

25a - 5b + c = 87

That's a second equation.

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The third point is (x,y) = (4,42).
So substitute 4 for x and 42 for y in

          y = ax² + bx + c

and get

         42 = a(4)² + b(4) + c
         42 = a(16) + 4b + c
         42 = 16a + 4b + c

Switch the left side with the right side:

16a + 4b + c = 42

That's a third equation.

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Put those three equations together as a system:


 4a - 2b + c = 18
25a - 5b + c = 87
16a + 4b + c = 42

Can you solve that system?  If not post again asking how.

Solution a = 3, b = -2, c = 2.  So

          y = ax² + bx + c

becomes

          y = 3x² - 2x + 2

Edwin