AQA A Level Maths: Pure复习笔记2.2.3 Completing the square
Completing the square
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 α ≠ 1
- You first need to take α 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
Exam Tip
- 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!
Worked Example
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