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

Step-by-step explanation:

the graph on the bottom right