This study notes covers Worked Example 2: Negative b 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 4 of 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example 2: Negative b
Write x² − 6x + 2 in completed square form
Solution
p = half of −6 = −3
(x − 3)² − (−3)² + 2
= (x − 3)² − 9 + 2
= (x − 3)² − 7
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