Polynomial Interpolation and Degree of the Polynomial

Question

I'm currently studying polynomial interpolation through Newton and Lagrange, and I've generated a polynomial approximation function with the following data points:

|  t  |  -1|-0.5 |-0.25|0.25| 0.5|  4|
|f(t) |-637|-96.5|-20.5|20.5|96.5|637|

I've generated the following interpolation polynomial with a degree of 5:

p(x) =−29.8236x⁵−29.8236x⁴+ 601.3198x³+ 9.3198x²+ 44.5340x−0.4659

I have plotted it using SciPy, and this is the graph p(x) generates:

Why does that behavior happen from t = 0.5 to t = 4?

Is it due to my polynomial being of a high degree? Should I try curve fitting instead?

EDIT: I inverted the table, as I was considering f(t) as t before.