Reminds me of the time that my daughter asked me how to solve a polynomial equation. Many moons removed from basic algebra I had to start from scratch and quickly ended up with the quadratic equation without realizing where I was going until the end. It was a satisfying experience although there’s no way to tell how much the work was guided by faint memories.
Having recently reverse-engineered the quadratic equation, it involves quite a few steps that would be pretty tricky to capture without a lot of time and patience, a very good intuition for algebra, or a decent guiding hand from past memories. Given how much of the structure I can recall from memory, the latter seems most likely, but it’s provably doable without knowing it in the first place, so I won’t dismiss that possibility :)
Reminds me of the time that my daughter asked me how to solve a polynomial equation. Many moons removed from basic algebra I had to start from scratch and quickly ended up with the quadratic equation without realizing where I was going until the end. It was a satisfying experience although there’s no way to tell how much the work was guided by faint memories.
Having recently reverse-engineered the quadratic equation, it involves quite a few steps that would be pretty tricky to capture without a lot of time and patience, a very good intuition for algebra, or a decent guiding hand from past memories. Given how much of the structure I can recall from memory, the latter seems most likely, but it’s provably doable without knowing it in the first place, so I won’t dismiss that possibility :)
It’s not too hard if you remember that you can get it from completing the square. Or of course you could use calculus.