Answer
f(x) = (x - 4)² - 67
Step-by-step explanation
We are asked to rewrite this function using the completing the square method.
f(x) = x² - 8x - 51
The first step in completing the square is to add and subtract the square of the half of the coefficient of x to the equation.
The coefficient of x = -8
Half of the coefficient of x = (-8/2) = -4
Square of the half of the coefficient of x = (-4)² = 16
f(x) = x² - 8x + 16 - 51 - 16
f(x) = x² - 8x + 16 - 67
f(x) = (x - 4)² - 67
Hope this Helps!!!