Completing the square (AQA GCSE Further Maths): Quizzes

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Completing the square
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What is the main goal of completing the square?

Transform x2+bx+cx^2 + bx + c into (x+p)2+q(x + p)^2 + q

What does 'equating coefficients' mean?

Making equal terms with same power

What is the expansion of (x−p)2(x - p)^2?

x2−2px+p2x^2 - 2px + p^2

For x2−6x+2=(x−p)2+qx^2 - 6x + 2 = (x - p)^2 + q, what is the value of pp?

33

For x2−6x+2=(x−p)2+qx^2 - 6x + 2 = (x - p)^2 + q with p=3p = 3, what is qq?

−7-7

For 2x2+bx+5=a(x−3)2+c2x^2 + bx + 5 = a(x - 3)^2 + c, what is the value of aa?

22

For 2x2+bx+5=a(x−3)2+c2x^2 + bx + 5 = a(x - 3)^2 + c with a=2a = 2, what is bb?

−12-12

What is the expansion of (x+b)2(x + b)^2?

x2+2bx+b2x^2 + 2bx + b^2

What order should you equate coefficients?

x2x^2 terms, then xx terms, then constants

What is a critical exam tip for completing the square?

Always expand brackets fully first

For 3x2+5x−1=a(x+b)2+c3x^2 + 5x - 1 = a(x + b)^2 + c, what is the value of aa?

33

For 3x2+5x−1=a(x+b)2+c3x^2 + 5x - 1 = a(x + b)^2 + c with a=3a = 3, what is bb?

56\frac{5}{6}

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