Finding a sixth degree polynomial that goes through 8 points

For a summative math research assignment, I will have to find a sixth degree polynomial that would ideally go through the following points: (0, 20.5625) (10, 27.5625) (30, 14.5625) (50, 14.6875) (60, 48.625) (73, 69.4375) (87, 43.9375) (100, 19)

The system, I believe, will look like: y1= a+bx+cx^2+dx^3+ex^4+fx^5+gx^6 I have not yet learned matrices, so solving this is quite hard for me. However, I am able to catch on quickly if your matrix answer is step-by-step.

Thank you so much!

• Anyway, your question is non-sense. Indeed, when $x=100$, $x^6=10^{12}$ and (using the Lagrange interpolation for example) you must work with $12$ significant digits; unfortunately, you have only $6$ significant digits ... – loup blanc Feb 10 '16 at 10:48

The system will look like you say, but the $x$'s have a subscript $1$ to match the $y$. There will be eight of those equations, one for each point, so you need eight constants to have a solution. You need an $hx^7$ term as well.
• @Narasimham: not if it is a polynomial in $x$. You are not allowed $xy$ terms and degree $n$ can only fit $n+1$ points – Ross Millikan Feb 10 '16 at 5:23