Supplementary Algebra

Cover Supplementary Algebra
Supplementary Algebra
Robert L Robert Louis Short
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Ii), we see that there are also two real intersections.
Note that the graphical method gives real inter- sections only. The reason is that our axes are Graphs.
19 chosen in a plane of real points, and imaginary points are in an entirely different field. Imagi- naries are plotted by what is known as the Argand diagram, but are not within the scope of the present paper.
Example. Plot }-^=i, and x^-\'r^=i6 25 9 on the same pair of axes. The result should give four rea/ intersections.
■ ■ I ' I I I
... I T' Fig. 12.
9. The Absolute Term. Determine what effect the absolute term has on the curve. Examine the curve j/=x^—x—i2 (Fig. 12). The curve turns at the point x=^y j/= — 12^, and when;ir=o, j^= — 12. Replace 12 by another constant, say 6. The curve now becomes j^=x^—x—6 (Fig. 13), which turns 20 Supplementary Algebra.
at the point x=^y j^ = — 6|, and crosses the j^-axis at —6. Replace 6 by o. Y^x^-'X — o (Fig. 14). This curve turns at ;r = |, 7 = — J, and crosses the axes at the origin.


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