グローバルビジネスで役立つ数学（85）グラフの対称移動（英語版）

Hi there!

Are you afraid of getting displaced from your post or totally displaced to leave the company? There might be some reasons you get replaced: poor performance or not being good at internal politics.

At the risk of repetition, I would say to become a globetrotter, you might want to become proactive, not reactive and passive. To be candid, it’s too late to take action after you’re told to step down the position or quit the company.

If you want to keep working in the same company, you must constantly enhance your skills and performance. If you have time to be scared of a doomsday, you should spend your precious time thinking positively and proactively about your upcoming plight.

Today, let me challenge myself to find the equation of a parabola by displacing it symmetrically. I can feel easy because I will not get into trouble even if I substitute the parabola wrongly.

Find the equation of a parabola obtained by displacing the parabola \(y = 3x^{2} – 3x + 3\) respectively based on (1) x-axis, (2) y-axis, and origin of the coordinates. (Ref: Yellow Chart Math Ⅰ＋Ａ P91, slightly changed the quadratic functions)

Here is my solution to the problem.

(1) x-axis
Just put a minus sign before \(y\), and so
\(-y = 3x^{2} – 3x + 3\)
Then, \(y = -3x^{2} + 3x – 3\)

(2) y-axis
Just plug \(-x\) in the original equation, and so
\(y = 3(-x)^{2} – 3(-x) + 3\)
Then, \(y = 3x^{2} + 3x + 3\)

(3) Origin
Put a minus sign before \(y\) and plug \(-x\) on the right side of the equation. So,
\(-y = 3(-x)^{2} – 3(-x) + 3\)
Then, \(y = -3x^{2} – 3x – 3\).

The related graphs are illustrated below.

Stay tuned, and expect to see my next post.

Keep well.

Frank Yoshida

￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
【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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