What is completing the square?
- Completing the square is another method used to solve quadratic equations
- It simply means writing in the form
- It can be used to help find other information about the quadratic like coordinates of the turning point
How do I complete the square?The method used will depend on the value of the coefficient of the x2 term in When a = 1
- p is half of the coefficient of b
- q is c - p2
When a ≠ 1
- You first need to take out as a factor of the x2 and x terms
- Then continue as above
When is completing the square useful?
- Completing the square helps us find the turning point on a quadratic graph
- It can also help you create the equation of a quadratic when given the turning point
- It can also be used to prove and/or show results using the fact that a squared term will always be greater than or equal to 0
- Sometimes the question will explicitly ask you to complete the square
- Sometimes it will even remind you of the form to write it in
- But sometimes it will expect you to spot that completing the square is what you need to do to help with other parts of the question... like finding turning points!