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Hey!

Where do I download programs for my HP Prime such as

Quadratic Formula
Area of a Triangle
Distance Formula
Arithmetic Series
Finite Geometric Series
Infinite Geometric Series
Volume of a Cone
Volume of a Sphere
Volume of a Pyramid
Area of a Sector
The best source of public-domain software for all recent HP programmable calculators is here:

https://www.hpcalc.org/

Either browse the Prime section, or use its search facility to look for specific programs.

Another great source for Prime software is the HP Prime Software Library right here in MoHPC:
https://www.hpmuseum.org/forum/forum-15.html

This too can be either browsed at your leisure, or searched using the built-in search engine (click on "Search" near the upper right corner).
Depending on just what you mean, many of those are built in. There is a built-in root finder that will essentially do the quadratic formula. for example.
Reference URL's