Student resource · Year 10 · PDF
Completing the Square When a > 1
Lesson breakdown Recall prior knowledge Review completing the square when the coefficient of x² is 1. Understand the challenge Explore why expressions such as 2x² + 12x + 5 cannot be completed by halving 12 immediately.
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What this is
Completing the Square When a > 1
Lesson breakdown
Recall prior knowledge
Review completing the square when the coefficient of x² is 1.
Understand the challenge
Explore why expressions such as 2x² + 12x + 5 cannot be completed by halving 12 immediately.
Factorise the leading coefficient
Take the coefficient of x² outside the first two terms:
2x² + 12x + 5 = 2(x² + 6x) + 5
Complete the square inside the brackets
Complete the square using the expression inside the bracket:
x² + 6x = (x + 3)² − 9
Manage the outer multiplier
Expand the multiplier carefully:
2[(x + 3)² − 9] + 5
= 2(x + 3)² − 18 + 5
= 2(x + 3)² − 13
Apply the method
Work through examples involving positive, negative and fractional constants.
Compare methods
Identify the difference between completing the square when a = 1 and when a > 1.
Practise and check understanding
Complete ordering, true-or-false, multiple-choice and exam-style tasks.
What students will gain
By the end of the lesson, students will be able to:
Factorise the coefficient of x² from the first two terms.
Complete the square inside brackets.
Manage the effect of an outer multiplier correctly.
Express a quadratic in the form a(x + p)² + q.
Identify the turning point of a quadratic from its completed square form.
Avoid common errors involving multiplication and constants.
Apply the method confidently to GCSE-style questions.
What you get
Apply the method
Work through examples involving positive, negative and fractional constants.
Compare methods
Identify the difference between completing the square when a = 1 and when a > 1.
Practise and check understanding
Complete ordering, true-or-false, multiple-choice and exam-style tasks.
What students will gain
By the end of the lesson, students will be able to:
Factorise the coefficient of x² from the first two terms.
Complete the square inside brackets.
Manage the effect of an outer multiplier correctly.
Express a quadratic in the form a(x + p)² + q.
Identify the turning point of a quadratic from its completed square form.
Avoid common errors involving multiplication and constants.
Apply the method confidently to GCSE-style questions.
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