To complete the square for the polynomial \( y^2 - 6y \), we need to take the coefficient of \( y \) (which is -6), divide it by 2, and then square the result.
- Take the coefficient of \( y \): \( -6 \).
- Divide by 2: \( \frac{-6}{2} = -3 \).
- Square the result: \( (-3)^2 = 9 \).
Now, we can complete the square by adding and subtracting this number inside the expression:
\[ y^2 - 6y + 9 - 9 \]
This can be rewritten as:
\[ (y - 3)^2 - 9 \]
Thus, the number that completes the square for the polynomial \( y^2 - 6y \) is 9.