1. ## Where's the roots?

Draw a single plot showing the parabola $f(x)=x^2-4x+5$ and where the roots are in relation to it.

2. Originally Posted by shawsend
Draw a single plot showing the parabola $f(x)=x^2-4x+5$ and where the roots are in relation to it.
There are no roots.

3. Originally Posted by malaygoel
There are no roots.
There are no real roots.

4. Hello, shawsend!

I don't know what they mean by "a single plot."
Since the roots are complex, how are we to graph them?

Draw a single plot showing the parabola $f(x)=x^2-4x+5$
and where the roots are in relation to it.

The roots are: . $x \:=\:2 \pm i$

Where are they? . . . Well, they are not on the $xy$-plane

If we had an $i$-axis coming out of the $xy$-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 $xy$-plane.

5. Originally Posted by Soroban
Hello, shawsend!

I don't know what they mean by "a single plot."
Since the roots are complex, how are we to graph them?

The roots are: . $x \:=\:2 \pm i$

Where are they? . . . Well, they are not on the $xy$-plane

If we had an $i$-axis coming out of the $xy$-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 $xy$-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 real-valued function and it's complex counterpart.