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Mathematics 87 Online
OpenStudy (anonymous):

What polynomial has a graph that passes through the given points? (-2, 2) (-1, -1) (1, 5) (3, 67) A. y = -x^3 + 4x^2 + 2x - 2 B. y = x^3 + 4x^2 + 2x - 2 C. y = x^4 + 4x^3 + 2x^2 - 2x D. y = x^3 - 4x^2 - 2x - 2

OpenStudy (anonymous):

This is basically a linera algebra problem where you have to solve 4 simultaneous equations in 4 variables (a, b, c, and d). The method is straightforward, but it is a lot of calculations, none of which are difficult. Just a lot of work. I'll outline what you have to do. You will have 4 equations, all of the form ax^3 + bx^2 + cx + d = y For each of the 4, you substitute the (x, y) point. The first point for the first equation, the second point for the second equation, etc. Now you have 4 equations in a, b, c, and d. Best to solve using Gaussian elimination. That is, you take any one of the equations and add/subtract a suitable multiple of that equation to the other 3 equations to make fall out of those 3 equations, whichever variable you select. That is now a "used euqation". Repeat 3 more times for the othe requations and variables.

OpenStudy (amistre64):

there are other ways to solve it which may or maynot be as labor intensive as a 4x4 matrix

OpenStudy (amistre64):

i like a newton method meself; given a set of points with x values {x1,x2,x3,...,xn} we can setup and solve (one by one if need be) the polynomial \[y = c_1 + c_2(x-x_1) + c_3(x-x_1)(x-x_2)+c_4(x-x_1)(x-x_2)(x-x_3)+... +(...)\]

OpenStudy (amistre64):

ran out of room :) but if none of these seem like a timely thing to accomplish on a test, you can always plug in the given points into the options and see what fits

OpenStudy (anonymous):

So is the answer c

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