Are quadratics really that important

If I was a student who had just finished a course in Algebra I in most schools across America I think that I would think that the following were the most important things that we had done. I would think this because we had spent so much of our efforts on it.

• linear equations
• distributive law
• quadratic equations
• factoring

The problem with this list isn't so much what is on it, it is what isn't on it. It seems to me that we simply must include exponential functions and therefore also logarithms. I guess my question is, "Are quadratics really that important?"

The only way to add these topics in is to take other topics away. So what can go? Here is a partial list of topics that might be cut or reduced in the standard curriculum.

• completing the square
• conics
• rational root theorem
• long division of polynomials

Exponentials seem like such a natural topic, and one that could be made to support and build on linear equations so beautifully. I will give more of this idea when I write later about "schlope".