This deep dive covers Method: When a = 1 within Completing the Square for GCSE Mathematics. Revise Completing the Square in Algebra for GCSE Mathematics with 10 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 2 of 6 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Method: When a = 1
To write x² + bx + c in the form (x + p)² + q:
1
p = half of b (the coefficient of x)
2
Write (x + p)² − p² + c
3
Simplify to get (x + p)² + q
Key insight: (x + p)² + q has turning point at (−p, q)
Practice questions for Completing the Square
To write x² + 10x + 3 in the form (x + p)² + q, what is the value of p?
Explain how you can tell from the completed square form whether a quadratic has a minimum or a maximum turning point.
Quick recall flashcards
Completing Square Formula
x² + bx + c = (x + b/2)² − (b/2)² + c. Halve b, square it, adjust constant.
Completing the Square
(x + p)² + q form. Half the b term, square it