Draw a single plot showing the parabola $\displaystyle f(x)=x^24x+5$ and where the roots are in relation to it.
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Draw a single plot showing the parabola $\displaystyle f(x)=x^24x+5$ and where the roots are in relation to it.
Hello, shawsend!
I don't know what they mean by "a single plot."
Since the roots are complex, how are we to graph them?
Quote:
Draw a single plot showing the parabola $\displaystyle f(x)=x^24x+5$
and where the roots are in relation to it.
The roots are: .$\displaystyle x \:=\:2 \pm i$
Where are they? . . . Well, they are not on the $\displaystyle xy$plane
If we had an $\displaystyle i$axis coming out of the $\displaystyle xy$plane,
. . the graph might look like this:
Code:y
 *

* *
* *
 * *
 *
 :
+   *     x
/ /
/ *
/ (2,0,1)
i/
One root is on the "floor" at (2,0,1).
The other is (2,0,1), one unit "behind" the $\displaystyle xy$plane.
. . . nicer please, as in a nice illustration which clearly and unambiguously depicts the parabola, the (complex) zeros, and their relationship to one another as an educational tool to help students make the connection between the realvalued function and it's complex counterpart.