Question 522737: how do i find the equation of the parabola, y=ax^2+bx+c, that passes through the following three points : (-2,40),(1,7),(3,15)?
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! how do i find the equation of the parabola, y=ax^2+bx+c, that passes through the following three points : (-2,40),(1,7),(3,15)?
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Substitute those value for x and y.
The solve the tree equations for a,b,c.
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ax^2 + bx + c = y
a(4) + b(-2)+c = 40
a(1) + b(1) +c = 7
a(9) + b(3) +c = 15
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I used a matrix method to solve the 3 equations and got:
a = 3
b = -8
c = 12
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Equation:
y = 3x^2-8x+12
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Cheers,
Stan H.
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Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Another method, using determinants:
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Parabola
x y x^2 Coeff
Point 1 -2 40 4 1
Point 2 1 7 1 1
Point 3 3 15 9 1
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I have an Excel sheet that does these.
--> y = 3x^2 - 8x + 12
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That was no help at all, except for confirming the solution.
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