Hi. This is more of a pre-calc question. I was asked to create a formula for a polynomial function with the following information: degree of 4, a zero at x=2, symmetric about the y-axis, vertical intercept at y=90, and a point at (-1, -60). From that, I gathered that since it is symmetric about the y-axis(even) that all powers must be even. Since it is a degree of 4, IF there is another zero, it can only be of the degree 4 or 2, and the zero I'm given can only be of the degree 4 or 2. Help!
Polynomial Formula
- Thread starter bree14
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Looks to me like you have the idea. I'll abuse the parameters a bit.
Degree 4
f(x) = ax^4 + bx^3 + cx^2 + dx + e
a zero at x=2
f(x) = (x-2)(ax^3 + bx^2 + cx + d)
what, specifically, do the other hints do?
Note: Symmetry gives you more information that you are imagining.
Steven G
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Let's build on what tkhunny gave you.
f(x) = (x-2)(ax^3 + bx^2 + cx + d). There are 4 unknowns, a, b, c and d (or are there that many?) You have two points, namely (0,90) and (-1,-60) and you know that there is symmetry about the y axis, that is for any number a we must have f(a) = f(-a). Now how do you use this info to find the value for a, b, c and d??
So, I can plug in those points and their inverses to the equation and use that to get the values? I understand that I would have to use a matrix or otherwise compare them in order to get each value. How do I do that when (0,90) is on the y-axis and is therefore the inverse is the same? Can I use my zero as a point?