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Question 384161: I know how to find the equation of a polynomial function when the zeros are given and there is a yintercept. The only thing that I dont know how to find an equation for is when the yintercept is at the origin or (0,0).
For example finding the polynomial equation where f(0)=f(5)=0 and f(2)=−12.I dont know if this is importent or is given from the answer but the degree has to be less then or equal to 2. This is very confusing to me. Please help explain to me. Thanks!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! finding the polynomial equation where f(0)=f(5)=0 and f(2)=-12.
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Using the form y = ax^2 + bx + c; (a 2nd degree equation)
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When the y intercept is 0, then c = 0, therefor the equation becomes just:
y = ax^2 + bx
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f(5)=0 then x=5; y=0
5^2a + 5b = 0
25a + 5b = 0
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f(2)=-12: x=2; y=-12
2^2a + 2b = -12
4a + 2b = -12
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Use elimination, multiply the 1st equation by 2, the 2nd equation by 5:
50a + 10b = 0
20a + 10b = -60
-------------------subtraction eliminates b, find a
30a = +60
a = 2
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Find b using the 1st equation:
25(2) + 5b = 0
50 + 5b = 0
5b = -50
b = -10
:
the equation: f(x) = 2x^2 - 10x
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