Answer :
we have the equation f(x) = 4x^2 - 16x + 27
Using the completing the square nethod
4x^2 -16x + 27
firstly, make sure the coefficient of x^2 is 1
divide all through by 4
4x^2/4 -16x/4 + 27/4
x^2 - 4x + 27/4 = 0
x^2 - 4x = -27/4
make the linear expression a perfect square
x^2 -4x/2 = -27/4
x^2 -(2x)^2 = -27/4
add the perfect square to both sides
x^2 -(2x)^2 = -27/4 + 4
(x - 2)^2 = -27/4 + 4
solving the Left hand side of the equation
-27/4 + 4
lcm is 4
-27 + 16/4/4
-11/4
(x - 2)^2 = -11/4
The vertex would lie when x = -2 and y =11
(-2 , 11)