Completing the Square (AQA A-Level Mathematics): Quizzes

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Completing the Square
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What is a complete square?

A squared bracket

What is (x+4)2(x + 4)^2 when expanded?

x2+8x+16x^2 + 8x + 16

Write x2+10xx^2 + 10x in the form (x+a)2+b(x + a)^2 + b.

(x+5)2−25(x + 5)^2 - 25

Complete the square for x2+14x−5x^2 + 14x - 5.

(x+7)2−54(x + 7)^2 - 54

Write x2+5xx^2 + 5x in the form (x+a)2+b(x + a)^2 + b.

(x+52)2−254(x + \frac{5}{2})^2 - \frac{25}{4}

What is the first step to complete the square for 3x2+18x−23x^2 + 18x - 2?

Factor out 3: 3(x2+6x)−23(x^2 + 6x) - 2

Complete the square for 2x2+8x+12x^2 + 8x + 1.

2(x+2)2−72(x + 2)^2 - 7

Write −x2+8x−3-x^2 + 8x - 3 in the form a(x+b)2+ca(x + b)^2 + c.

−(x−4)2+13-(x - 4)^2 + 13

Find the vertex of y=(x−5)2+7y = (x - 5)^2 + 7.

(5,7)(5, 7)

What is the line of symmetry for y=(x+3)2−8y = (x + 3)^2 - 8?

x=−3x = -3

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