Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

y2 − 6y +

Answer 1

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.

1. Take the coefficient of \( y \): \( -6 \).
2. Divide by 2: \( \frac{-6}{2} = -3 \).
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**.