Completing the square - in the form
Write a monic quadratic as a squared bracket plus or minus a constant.
- Halve the coefficient of
to get the number inside the bracket. - Squaring that bracket introduces an extra constant. Subtract it, then include the original constant.
- The result has the form
.
Example 1
An even coefficient
Complete the square.
Example 2
An odd coefficient
Write the expression in completed-square form.
Remember
The sign goes inside the bracket too: half of
Your turn
Question 1
Complete the square.
Check answer
Question 2
Complete the square.
Check answer
Question 3
Complete the square.
Check answer
Question 4
Complete the square.
Check answer
Question 5
Complete the square.
Check answer
Complete the square.
Complete the square.
Complete the square.
Complete the square.
Complete the square.