Consider the quadratic function

y1 = (x - a)^2+ b^2 , where a , b are real numbers.

-Write down the coordinates of the vertex.
-Show that y1 has zeros a +/- ib , where i = root(-1) .

The “shadow function” to y1 is another quadratic y2 which shares the same vertex as y1 .
However, y2 has opposite concavity to that of y1 and its zeros are in the form a +/- b .
Use various values for a and b to generate pairs of functions y1 and y2 .

Question

Consider the quadratic function

y1 = (x - a)^2+ b^2 , where a , b are real numbers.

 -Write down the coordinates of the vertex.
 -Show that y1 has zeros a +/- ib , where i = root(-1) .

The “shadow function” to y1 is another quadratic y2 which shares the same vertex as y1 .
However, y2 has opposite concavity to that of y1 and its zeros are in the form a +/- b .
 Use various values for a and b to generate pairs of functions y1 and y2 .