Question

What polynomial has a graph that passes through the given points?
(-4,89)(-3,7)(-1,-1)(1,-1)(4,329)
how would I start this?

Answer 1

@amistre64 had a quick and snappy way to do this that i forget
you have to set up a system of equations
start by calling your polynomial
\[p(x)=ax^4+bx^2+cx+d\] and then fill in the numbers you know

Answer 2

for example since \((1,-1)\) is on the graph, you know that
\[p(1)=a+b+c+d=-1\] so there is one equation

Answer 3

damn typo there i am missing a cube term!

Answer 4

\[p(x)=ax^4+bx^3+cx^2+dx+e\]\[p(1)=a+b+c+d+e=-1\]
\[p(-1)=a-b+c-d+e=1\] etc etc
it is a pain

Answer 5

if it was me, i would cheat and be done in one second

Answer 6

yeah no kidding.... I

Answer 7

http://www.wolframalpha.com/input/?i=polynomial+%28-4%2C89%29%28-3%2C7%29%28-1%2C-1%29%281%2C-1%29%284%2C329%29

Answer 8

apparently the answer is \[x^4+2 x^3-3 x^2-2 x+1\]

Answer 9

Aren't we checking a polynomial equation, not a polynomial expression?

Seems to me that with five points on the graph, we'd end up with five equations in five unknowns, which to me signifies y = ax^4 + bx^3 + cx^2 + dx^1 + e (which has five unknown coefficients). So, each of the five points must satisfy the equation
y = x4+2x3−3x2−2x+1.

Think: how'd you solve a system of five linear equations in five unknowns? Personally, I'd use matrices.