Tangents of a parabola

I apologize to readers of this blog for my month's absence. My Internet provider was down for about eleven days and I prioritized the science fiction blog instead of this one.

Over the next few days, I'm going to play with describing a function using just the tangent lines. The first function is a parabola y = x² with x between -1 and 1 in increments of 0.1. Since this uses a total of 21 lines, I decided to use a seven colored rainbow sequence (ROY G. BIV for all you spectrum nerds out there) where three consecutive lines are red, then three orange, etc.
 

The second version of the idea still uses ROY G. BIV, but each line is a different color from the previous.

I think these are pretty and I'm going to try some other functions as well over the next few days.