Rewrite the function by completing the square. f (x) = x 2 - 8 x - 51 f (x) = x 2 - 8x-51

(x-4) ^2 - 67

Step-by-step explanation:

f (x) = x^ 2 - 8 x - 51

Take the coefficient of x

-8

Divide by 2

-8/2 = - 4

Square it

(-4) ^2 = 16

Add this and subtract it

f (x) = x^ 2 - 8 x + 16 - 16 - 51

= (x^2 - 8x+16) - 67

= (x-4) ^2 - 67