グローバルビジネスで役立つ数学（81）２次関数の軸と頂点（英語版）

Hi there!

Described below is one of the F.A.Q.s to me by my online students:

――When was your best time while working at a trading company?

You know, “best time” can be construed in many ways, and I guess you also find it tough to answer loud and clear. However, I can respond immediately without any hesitation: “Now!” In other words, my best time was not at my trading company.

――How come?

Because I am learning all the time. The tombstone will be my diploma.

In my early twenties, I was a frequent flyer overseas when the company used to export scads of home electronic appliances in containers. If I remember correctly, one of the clients was called “Zenith,” with whom we were doing O.E.M. business.

We highly savored the export-led business and fizzed with life even in offering prices to clients worldwide. As the client’s name implies, we were forthright in the middle of the vertex of business in whichever place we were, domestic or overseas. It was the time when I started to have my self-esteem as a Shoushaman.

Today, remembering the heyday of the export business, let me challenge myself to find the vertex of a quadratic equation and its axis.

Draw the graph of the quadratic function \(y = -5x^{2} + 12x – 7\), and find its axis and vertex. (Ref: Yellow Chart Math Ⅰ＋Ａ P87, slightly changed the condition)

Here is my solution to the problem.

\(y = -5x^{2} + 12x – 7\)
\(= -5(x^{2} – \frac{12}{5}x) – 7\)

By completing the square of the quadratic equation,
we get \(y = -5(x -\frac{6}{5})^{2} + \frac{1}{5}\).

Therefore, its graph becomes as shown below.

And the axis is the straight line \(x = \frac{6}{5}\), and the vertex becomes the coordinate \((\frac{6}{5}, \frac{1}{5})\).

Am I better install a satellite dish to receive the frequency of an elusive blue ocean business down the road?

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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