What is the axis of symmetry for the function f(x) =-2x^2+4x+1 is the line x=1 where is the vertex of the function located?

Step-by-step explanation:

hello :

f(x) =-2x²+4x+1       Completing The Square : f(x) =2(x²+2x)+1

f(x) = -2((x²-2x+1)-1)+1

f(x) = -2((x-1)²-1)+1

f(x) =2(x-1)²+1  ... verex form   when the vertex is (1,1)

the axis of symmetry  is x=1

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x