Complete the square for the function Complete the square for

Complete the square for the function

Complete the square for the function f(x) = -4x^2 + 8x - 1

Solution

F(X) = -4x^2 +8x -1

To make it perfect square , let take out -ve sign as common outside the

bracket:

f(x) = -( 4x^2 -8x +1)

as compared to (a-b)^2 = a^2 +b^2 -2ab

we have a = 2x ; 2ab = 8 , we need to make the b^2 term suc that b= 2

So, f(x) = -(4x^2 -8x +1 +3 -3) =  -(4x^2 -8x +1 +3 -3)

= -(4x^2 -8x +1 +3) +3

= -(4x^2 -8x +4) +3

f(x) = -(2x -2)^2 +3