When I was in school, I was taught the Quadratic Formula. I was taught that it was the most efficient, more reliable way to find the roots of a quadratic function. This is what I was taught: Given a function in Standard Form, \(ax^2+bx+c\), its roots can be found by evaluating \(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\). I was instructed…
Author: Clio
What’s in a Name?
I’ve been thinking a lot lately about my name. My legal name is “Paul”. It’s the name I’ve worn most of my life. When I was too young to remember, I was Timmy. That was based on my middle name, which is Timothy. My older brother went by Mark, his middle name, and I went…
Proof: The rationality of the y-intercept
Theorem: Given a quadratic function with rational roots, the \(y\)-intercept is rational if and only if the stretch is rational. Proof: If \(f\) is a quadratic function with rational roots \(m\) and \(n\) and vertical stretch \(a\), then \[f(x) = a(x – m)(x – n) \\ = a(x^2 – (m+n)x + mn) \\ = ax^2…
I will do my best to be kind to you.
I will do my best to be kind to you. It’s hard, sometimes. I am so used to people wanting to hurt me. I am so used to people wanting to be cruel to others. It is so hard to see that cruelty and say, I will do my best to be kind to you….
Paper Jack
Paper Jack had a secret: He lived on a piece of paper. You might have thought that was obvious from his name, but the truth is, his friends didn’t know. They thought his name was some sort of clever, hipster nickname. Like Two Fingers Tommy or Rick the Knife. Two Fingers Tommy didn’t really have…
i am
i am devoured i am exhausted i am denied that which i have been i am relegated to the edges i am devoted i protect my charge and when she whispers i elevate her voice until it shimmers and shatters and tears itself asunder i am legion i am nothing i am left to scrape…
the name that i have been given
the name that i have been given speaks to a child that doesn’t understand the cruelty of the world as if it is a given as if that is how the world must be as if the child is the one that is broken because they cannot understand you might say it in the space of a heartbeat…
Functions and Domains: The Other Shoe
I have taught high school mathematics for nearly a decade. I have a BS in Mathematics. The Algebra II curriculum, which I largely built for my school, is based on “the story of functions”. And yet, it was only the other day that I noticed something that was woefully wrong about the way that I’ve…
i have a poem
i have a poem sitting on my tongue like the eucharist and it melts into my skin even as i try to expel it i want to let these tears go but they stick to my cheeks like icicles that crack with my forced smile these words used to matter but they’ve folded into themselves…
Rate of Change and the Power Rule
I’ll keep this one short. Also, it’s on calculus, for whatever that’s worth. The Power Rule for Differentiation says that the derivative of a monomial \(ax^b\) is \(abx^{b-1}\). Last night I noticed a way to derive this for positive integers that I believe I’ve seen before (so I’m not claiming originality), but which is different…