Final answer:
To complete the square for -z² + 4z, we need to rewrite the expression in the form (z - h)² + k. By factoring out -1 and finding the value of h, we can write the expression as (z - 2)² - 16.
Step-by-step explanation:
The given expression is -z² + 4z. To complete the square, we need to rewrite the expression in the form (z - h)² + k, where h and k are constants. Let's first factor out -1 from the expression: -1(z² - 4z).
Next, we need to find the value of h by dividing the coefficient of z by 2 and squaring it. In this case, the coefficient of z is -4, so h = (-4/2)² = 4² = 16.
Lastly, we add and subtract 16 inside the parentheses to maintain the same expression: -1(z² - 4z + 16 - 16) = -1((z - 2)² - 16).
Therefore, the completed square form of -z² + 4z is (z - 2)² - 16, which corresponds to option c) -(z - 2)².