Question 138917: heres the question: FInd a quadration function that fits the set of data points (0,-9),(-2,-13),(3,27) please help I have no idea how to do this.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! FInd a quadratic function that fits the set of data points:
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(0,-9),(-2,-13),(3,27)
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One way is write 3 equations in the form: ax^2 + bx + c = y
Find a, b, and c. We know c which is the y intercept, which occurs when x = 0
Therefore c = -9, we only need to deal with two equations using the 2nd & 3rd coordinates
:
Substitute -2 for x and -13 for y:
a(-2^2) + b(-2) - 9 = -13
4a - 2b - 9 = -13
4a - 2b = -13 + 9
4a - 2b = -4
Simplify, divide equation by 2
2a - b = -2
:
The 3rd set of coordinates, Substitute 3 for x and 27 for y:
a(3^2) + b(3) - 9 = 27
9a + 3b = 27 + 9
9a + 3b = 36
Simplify, divide equation by 3
3a + b = 12
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Use elimination on these two equations to find a
2a - b = -2
3a + b = 12
---------------adding eliminates b
5a + 0 = 10
a =
a = +2
;
Use the equation 3a + b = 12 to find b, substitute 2 for a
3(2) + b = 12
b = 12 - 6
b = 6
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Our equation then is: y = 2x^2 + 6x - 9
:
you should confirm this by substituting each x value of the given coordinates
and confirm that the equation equals the given y value
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If you follow all this, it will go a long way toward you understanding quadratic equations. You can email me if you have a question about this.
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