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

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: What is the equation of a parabola that passes through the points (1,6),(-2,27), (2,11)?      Log On


   

Question 28016: What is the equation of a parabola that passes through the points (1,6),(-2,27), (2,11)?
Answer by bmauger(101) About Me  (Show Source):
You can put this solution on YOUR website!
A quadratic equation can be written in the form
y=ax%5E2%2Bbx%2Bc By putting in the three points given we can get three linear equations of the three variables a, b, & c and then solve:
evaluating
y=ax%5E2%2Bbx%2Bc for (1,6) we get:
6=a%281%29%5E2%2Bb%281%29%2Bc or
Eq 1: 6=a%2Bb%2Bc
For (-2, 27)
27=a%28-2%29%5E2%2Bb%28-2%29%2Bc
Eq 2: 27=4a-2b%2Bc
For (2, 11)
11=a%282%29%5E2%2Bb%282%29%2Bc
Eq 3: 11=4a%2B2b%2Bc
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:
11=4a%2B2b%2Bc
-6=a%2Bb%2Bc
=5=3a%2Bb
and then subtract equation 1 from equation 2 to get:
27=4a-2b%2Bc
-6=a%2Bb%2Bc
=21=3a-3b
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: y=ax%5E2%2Bbx%2Bc and that's your answer (unless you're supposed to factor or find the roots, graph it, or do anything else to the equation).