SOLUTION: y=-2(x-(3+i))(x-(3-i)) a. What are the zeros of the quadratic function? b. Write the quadratic function in standard form.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: y=-2(x-(3+i))(x-(3-i)) a. What are the zeros of the quadratic function? b. Write the quadratic function in standard form.       Log On


   

Question 1060935: y=-2(x-(3+i))(x-(3-i))
a. What are the zeros of the quadratic function?
b. Write the quadratic function in standard form.

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
(a) You already have the factorization, so this part of the question is already shown.

(b) First try simplifying, ....
y=-2%28x-3-i%29%28x-3%2Bi%29
-2%28%28x-3%29-i%29%28%28x-3%29%2Bi%29
-2%28%28x-3%29%5E2-i%5E2%29
-2%28%28x%5E2-6x%2B9%29%2B1%29
-2%28x-3%29%5E2-1%2F2%29
highlight%28y=-2%28x-3%29%5E2-1%2F2%29-----standard form


Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
(b) 

   y = -2(x-3-i)(x-3+i) =


     = (-2)((x-3)-i)((x-3)+i) = 


     = %28-2%29%28%28x-3%29%5E2-i%5E2%29 = 

     = %28-2%29%28%28x%5E2-6x%2B9%29%2B1%29 = 

     = -2x%5E2+%2B+12x+-+20

       highlight%28y=+-2x%5E2+%2B+12x+-+20%29   -----standard form

What "josgarithmetic" produced is a vertex form.