Finding a,b, and c in quadratic equation with only list of coordinates?

Pick 3 of the points and substitute them for (x, y) in the standard form quadratic equation.

2.7 = a(1^2) + b(1) + c

6.9 = a(2^2) + b(2) + c

13.9 = a(3^2) + b(3) + c

Solve the system of equations for a, b, and c.

First, your list of coordinates got cut short by Yahoo! for being too long. You need to insert some blank spaces so it doesn't look like one long nonsense word.

Plug (1, 2.7) into the general quadratic equation y = ax² + bx + c:

a1² + b1 + c = 2.7

which simplifies to

a + b + c = 2.7

Do the same for (2, 6.9):

4a + 2b + c = 6.9

Do the same for (3, 13.9):

9a + 3b + c = 13.9

Now you have a system of three equation with three unknowns. (You could have used any three points from the curve.)

Solving the system is hard to explain here!--but your teacher must have covered this. The solution is

a = 1.4

b = 0

c = 1.3

so the quadratic equation becomes

y = 1.4x² + 1.3

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