Write a polynomial function in standard form with real coefficients whose zeros include 2 comma 7 i comma and negative 7 i .

This will be a third degree polynomial since we have 3 zeros.  We will FOIL them out.  They are: (x-2), (x+7i), (x-7i).  The product of the second and third factors gives us .  i^2 = -1, so if we simplify, we have .  Now we will multiply that with x-2 to get .  There you go!

Do you need with the x value for the minimum? its always between the two intercepts for a parabola