## A Problem with Parabolas

Let $P$ be the parabola with equation $y=x^2$ and let $Q$ be a parabola with a horizontal axis of symmetry. Suppose that $P$ and $Q$ intersect at $(1,1)$, $(3,9)$, and at one other point. Find the equation of the axis… Continue Reading

Astute geometry students know that when a problem involves a 3 and a 4, the answer will involve a 5 and the solution will make use of a right triangle somehow. The triple of numbers $(3,4,5)$ is called a Pythagorean… Continue Reading

## Plane Vectors

About a year ago, I was trying to teach my students about vector addition when I found this video on CNN, which does a wonderful job of depicting vector addition problems in real life. The plane is trying to fly… Continue Reading

## Derivatives Without Limits, Part 3

In my last post, I talked about how one could guess the equation of the tangent line to a polynomial and then check whether that guess is right by factoring. Let us now turn to the question of computing the… Continue Reading

## Derivatives Without Limits, Part 2

In my last postÂ I talked about how to verify that a point on the graph of a cubic polynomial was a local minimum using only techniques from algebra. We will now try to generalize our methods a bit to be… Continue Reading

## Derivatives Without Limits, Part 1

First off, welcome to my blog, and thanks for reading! My purpose with this blog is to talk about the things that interest me as a teacher, which is mainly advanced mathematics and helping students understand it. Today in calculus… Continue Reading