Need help with a Polynomial Function Graph given the points

Nov 2019
6
0
California
Easier to work with it in factorised form.
Because it is a fourth degree polynomial with factors of (x-2) raised to an even power and (x+4) raised to an even power then
\(\displaystyle f(x) = a(x-2)^2(x+4)^2\) to give a fourth degree polynomial (when expanded out).

Your job now is to find a such that the graph goes through (0, 16).
That helped tremendously. I found a to equal 0.25
 

Debsta

MHF Helper
Oct 2009
1,313
600
Brisbane
Perfect. So now you have the equation in factorised form. Up to you if you want to expand it out. You can enter it into desmos in factorised or expanded form.