Question 460073: I am having a hard time with quadratic equations, can someone help me.
Find the quadratic equaton that fits the following set of data points
((-1,-5),(-4,59),(-3,37))
Thank you
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Since we're forcing a parabola to go through these three points, this means that when we plug in each 'x' into the general formula  , we'll get 'y'. So essentially, we're plugging in corresponding values of 'x' and 'y' and forming equations, which we'll use to solve for 'a', 'b', and 'c'.
So for instance, if we plug in x=-1, then we'll get the output of y=-5. This means that
 which simplifies to 
Do the same with the second point to get the second equation 
Finally, do the same with the third point to get the third equation 
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After doing all that, we have the system
which translates into this augmented matrix
Row reduce this matrix (see this image for full steps on how to do that) to get
Note: alternatively you can use a calculator to do the row reduction.
The last column represents the values of 'a', 'b', and 'c' respectively.
So  ,  and 
So the quadratic equation that goes through the three given points is 
As a check, if we plug in x = -1, then....
So plugging in x = -1 gives us y = -5, meaning that the point (-1,-5) lies on the parabola. This partially verifies our answer.
Do the same with the other two points to verify this equation actually works.
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