グローバルビジネスで役立つ数学（79）グラフの移動（英語版）

Hi there!

On a Sunday at noon in Djibouti, Africa, I slacked off and hung loose on a bench in a small park with a cigarette dangling from my lips.

The shower fittings in my hotel room broke, making me nerve-wracked. For the bathroom, “unhygienic” is, to put it mildly; it was beyond the limit of my patience.

I was sitting awkwardly for an hour or so when a French couple came up to me and said,

――Êtes-vous un Japonais ?

“Japonais” sounded comprehensible for me to understand “Japanese,” so I answered “Oui” without any delay.

We enjoyed conversations using gestures for a while, and finally, they invited me to dinner at their house. The husband was a fighter pilot of the French Airforce and told me they would stay a year or so for some reason.

Thanks to their entertainment, I could feel better about staying in Djibouti by thinking that nothing ventured, nothing gained. I had decided to extend the same kindness to someone else somewhere down the road.

A few years later, since I came back to Japan, I invited some American students to my apartment for dinner who apparently looked lonely in Japan. They thanked me so much and, knowing what happened to me in Djibouti, taught me that’s “paying it forward.”

We, humans, are sometimes spiritually precarious; however, I realized we could start again from scratch by paying it forward. Kindness is its own reward; that’s what I learned.

Today, let me challenge myself to find the equation of a parabola obtained by displacing its original equation symmetrically across the origin.

Find the parabola equation obtained by displacing the original parabola \(y = -2x^{2} + 1\) symmetrically across the origin. (Source: Yellow Chart Math Ⅰ＋Ａ P83)

Here is my solution to the problem.

We have \(f(x) = -2x^{2} + 1\), so the function to be obtained should be \(-y = f(-x)\).

Then, \(-y = -2(-x)^{2} + 1\).
Therefore, \(y = 2x^{2} – 1\).

I’ll start all over again from October 1, 2022. I am excited about thinking about how I will pay it forward.

Stay tuned, and expect to see my next post.

Keep well.

Frank Yoshida

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【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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