This Demonstration shows the graphs of two symmetric quadratic functions (with respect to the

axis) of the form

and

, where

and

are the horizontal and vertical translations of the corresponding parabolas

and

, with vertices at the origin. Their complex zeros are identical and marked by red dots located in the complex plane

, where the

and

axes (labeled in red on the graph) coincide with the Cartesian plane

coordinate

and

axes; that is, the

axis is also the real axis and the

axis is also the imaginary axis. While any real zeros lie on the

axis (or real axis), imaginary zeros come in pairs (complex conjugates) and lie on the vertical line

that runs through the vertices (and foci) of the parabolas. Further, as complex conjugates, the zeros are symmetric with respect to the

axis (real axis). To see the effects on the graph when

, click on the checkbox "force

to equal

(vertices = zeros)" and move the

slider.