SOLUTION: How do you find the equation of a parabola that passes through the points (5,3) (3,6) and (-4,5) ?

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Question 813219: How do you find the equation of a parabola that passes through the points (5,3) (3,6) and (-4,5) ?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Use general form ax%5E2%2Bbx%2Bc=y for each point and solve simultaneous equations which these points produce. Your variables are now a, b, and c. You might want to set up as a matrix and perform elementary row operations.

Refine this system:
a5%5E2%2Bb%2A5%2Bc=3
a3%5E2%2Bb%2A3%2Bc=6
a%28-4%29%5E2%2Bb%28-4%29%2Bc=5

System:
25a%2B5b%2Bc=3
9a%2B3b%2Bc=6
16a-4b%2Bc=5
You might want to use some matrix handling software to solve the system.

After that, work with it any way you want.


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Using the matrix calculator page, http://www.math.purdue.edu/~dvb/gaussian.php
Values obtained were a=-.01825, b=-0.0397, c=7.7619