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# Polynomial Table Ordered Pairs Help!!

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140
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Hi math whizzes,

Could you help me out with this homework problem and concept?

Nov 7, 2018

#1
+98044
+2

It crosses the x axis at x  = - 1

The...it  crosses the x axis again at x = 1

And f(-2) =  f(2)

So.....this appears to be a quadratic  [ a parabola that turns upward ]  =  degree 2

Nov 7, 2018
#2
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The function can't be a quadratic.

Guest Nov 7, 2018
#3
+4402
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boo CPhill, enough of these have been done that I'd have thought you'd seen one by now.

You need to take successive adjacent differences of f(x)

$$\left( \begin{array}{c} \{30,0,-2,0,30,160,510\} \\ \{30,2,-2,-30,-130,-350\} \\ \{28,4,28,100,220\} \\ \{24,-24,-72,-120\} \\ \{48,48,48\} \\ \end{array} \right)$$

in the matrix above the first line is f.

successive lines are formed by taking the line above minus it shifted 1 place to the left

that we could do this 4 times before all the numbers were equal shows that f is degree 4

Nov 7, 2018
#4
+98044
+2

I just "eye-balled" it...and didn't have time to go through the sum-of-differences thing