Free taster
5 of 6 sections open
A Perfect Form
A Perfect Form
x² + 6x + 9 = (x + 3)². That's a "perfect square". But what about x² + 6x + 5? It's not perfect... yet! Completing the square lets us rewrite ANY quadratic in a perfect form, revealing the turning point of its graph.
Method: When a = 1
To write x² + bx + c in the form (x + p)² + q:
Now try it yourself
Quiz · Question 1 of 10
To write x² + 10x + 3 in the form (x + p)² + q, what is the value of p?
Tap an answer to check it
This topic in real past papers
Every real exam question we've found on completing the square, with a full worked answer.
AQA Paper 1
Three of the four sittings we have full papers for use the completed square form directly, either to solve an equation, express an expression, or find a turning point.
Edexcel Paper 1
All three sittings we have full papers for use an algebraic method on a quadratic, and each sitting tests a different specific technique.