SOLUTION: a funtion has three x intercepts at x=-2 x=1 and at x=5 if g(2)=-4 give a possible equation
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Question 776705: a funtion has three x intercepts at x=-2 x=1 and at x=5 if g(2)=-4 give a possible equation
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If there are intercepts at (-2,0), (1, 0), and (5,0), then a polynomial that fits must have factors of )
, )
, and )
, hence a function that fits the data is \ =\ k(x\ +\ 2)(x\ -\ 1)(x\ -\ 5))
.
Then if \ =\ -4)
we know:
\ +\ 2)((2)\ -\ 1)((2)\ -\ 5)\ =\ -4)
Solve for 
and then multiply the three binomials, collecting like terms and distribute
========================
Alternate solution.
You have four non-collinear data points, so there exists a 3rd degree polynomial function that exactly models the data.
The general form of a cubic polynomial is:
\ =\ ax^3\ +\ bx^2\ +\ cx\ +\ d)
So, if the point (-2, 0) is on the graph of the polynomial, then it must be true that:
Likewise, considering the other given points,
And
Solve the 4X4 system to find the coefficients of the desired polynomial.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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