Create the quadratic function that contains the points (0, -2), (1, 0) and (3, 10). show all of your work for full credit

My graphing calculator tells me the function is
.. f(x) = x^2 +x -2

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Since we recognize the y-intercept as being (0, -2), we only need to find the coefficients of x and x^2.

If you want to do this by hand, you can use
.. y = ax^2 +bx -2
to write 2 equations in a and b for the (x, y) values (1, 0) and (3, 10).
.. 0 = a +b -2
.. 10 = 9a +3b -2
To solve by substitution, you can let a = 2-b, and you have
.. 10 = 9(2 -b) +3b -2
.. 6b = 6 . . . . . . . . . . . add 6b-10
.. b = 1
.. a = 2 -1 = 1