y= -4x² - 16x - 14
Take the coefficient of x² as the common factor
y = - 4(x² + 4x + 7/2)
Add (b/2)² to complete the square
y = - 4( x² + 4x + 2² - 2² + 7/2)
Complete the square
y = -4( (x + 2)² - 1/2)
Remove the bracket
y = -4(x + 2)² + 2
Answer: y = -4(x + 2)² + 2