Hi there!
No one wants to get demoted or relegated to a branch office in a rural area. Me either, providing I wish to stick to the company I work for.
Fortunately, I’ve never faced such a sober reality; instead, the fact to be told, I took action proactively so that I could manage to put myself away from its floating world or mundaneness.
To put it precisely, I might be crafty or scared.
I’ve seen several ex-coworkers relegated or demoted to the rank-and-file position. Surprisingly, the reasons for it were all convincing, taking into consideration the poor performances that they have done.
Today, let me challenge myself to identify how the original parabola moved on the coordinate graphics by paying attention to the x- and y-axis.
Use coordinates to answer how to move the graph (Ⅰ) \(y = x^{2} – 3x + 3\) to the graph (Ⅱ) \(y = x^{2} + 4x + 2\). (Ref: Yellow Chart Math Ⅰ＋Ａ P89, slightly changed the quadratic functions)
Here is my solution to the problem.
First of all, from (Ⅰ),
\(y = x^{2} – 3x + 3 = (x – \frac{3}{2})^{2} + \frac{3}{4}\)
Put the vertex of the parabola (Ⅰ), A, then
\(A(\frac{3}{2},\,\frac{3}{4})\).
From (Ⅱ),
\(y = x^{2} + 4x + 2 = (x + 2)^{2} – 2\)
Put the vertex of the parabola (Ⅱ), B, then
\(B(-2,\,-2)\).
Taka a look at the difference in the vertex coordinates between the parabola (Ⅰ) and the parabola (Ⅱ),
\(-2 – \frac{3}{2} = -\frac{7}{2}\),
\(-2 – \frac{3}{4} = – \frac{11}{4}\)
Therefore, move the parabola (Ⅰ) by \(-\frac{7}{2}\) in the direction of the x-coordinate and by \(-\frac{11}{4}\) in the order of the y-coordinate to get the parabola (Ⅱ).
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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