SOLUTION: Examine the quadratic relation y=4x^2-4x+1 a) express the relation in factored form b) determine the zeros. c)Determine the coordinates of the vertex.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Examine the quadratic relation y=4x^2-4x+1 a) express the relation in factored form b) determine the zeros. c)Determine the coordinates of the vertex.      Log On


   

Question 1118619: Examine the quadratic relation y=4x^2-4x+1
a) express the relation in factored form
b) determine the zeros.
c)Determine the coordinates of the vertex.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=%282x-1%29%5E2


2x-1=0
2x=1
x=1%2F2-------the only zero


vertex: ( 1/2, 0 )

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
y = 4x%5E2+-+4x+%2B+1 = %282x-1%29%5E2.


The root is  x = 1%2F2 = 0.5.   It is only one (merged) root.


The coordinates of the vertex are  (x,y) = (0.5,0).


Be aware:   The answer by  @josgaritmetic   i s   i n c o r r e c t.