Question 1176849: The figure above shows the plot of the points (1,6), (2,3), (3,5), (4,7), and (7,9). Find a polynomial of degree 4 of the form f(x)=ax^4+b^3+cx^2+d+e whose graph passes through these points.
f(x)=
Answer by Solver92311(821)   (Show Source):
You can put this solution on YOUR website!
We are used to looking at ordered pairs as ) , but for this problem, it would be helpful to consider an ordered pair to represent \)) which is to say that the first value is a value in the domain of  and the second value is the value of the function at that input value. In other words, if ) is a point on the graph of some function , then \ =\ 6) .
Given that, if
\ =\ ax^4\,+\,bx^3\,+\,cx^2\,+\,dx\,+\,e)
and the point ) is on the graph of the function then it must be true that:
^4\,+\,b(1)^3\,+\,c(1)^2\,+\,d(1)\,+\,e)
Which simplifies to
Similarly,
^4\,+\,b(2)^3\,+\,c(2)^2\,+\,d(2)\,+\,e)
Which simplifies to
And so on for the other 3 given points.
Once you have the 5 linear equations in the 5 variables a, b, c, d, and e, solve the 5X5 system for the 5 values and use these values for the coefficients when writing the specific definition of ) . There are several on-line linear system solvers and I would recommend using one of them since the coefficients in your linear system are going to get very big before you are through and the arithmetic will be uglier than a mud fence. Good luck.
John
My calculator said it, I believe it, that settles it
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