SOLUTION: What is the equation of a parabola that passes through the points (1,6),(-2,27), (2,11)?

Question 28016: What is the equation of a parabola that passes through the points (1,6),(-2,27), (2,11)?
Answer by bmauger(101) (Show Source): You can put this solution on YOUR website!
A quadratic equation can be written in the form
By putting in the three points given we can get three linear equations of the three variables a, b, & c and then solve:
evaluating
for (1,6) we get:
or
Eq 1:
For (-2, 27)

Eq 2:
For (2, 11)

Eq 3:
Now you simply solve the three simolutanious equations for a, b, and c.
To get you started, let's subtract equation 1 from equation 3 to get:

-
=
and then subtract equation 1 from equation 2 to get:

-
=
Using the two new equations we found should be enough to get you to the answer in a few more steps. When you get there put your a, b, and c in for: and that's your answer (unless you're supposed to factor or find the roots, graph it, or do anything else to the equation).
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