AQA, OCR, Edexcel GCSE GCSE Maths

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AQA, OCR, Edexcel

GCSE GCSE Maths

Completing the Square Hard Answers

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Total Marks: /26

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Completing the Square (Hard)

1. Write 22 + 7 - 3 in the form ( + )2 + . 7 2 73

2 ( + 4) - 8 (4 Marks)

2. a. Write 22 + 9 + 1 in the form ( + )2 + . 9 2 73

2 ( + 4) - 8 b. Hence solve 22 + 9 + 1 = 0 , leaving your answer in surd form.

(5 Marks)

9 73

73 9

= - 4 - 4 , = 4 - 4

3. A curve has an equation = 22 - 5 + 12. a. Write = 22 - 5 + 12 in the form = ( + )2 + . 5 2 71 = 2 ( - 4) + 8 b. Find the coordinates of the minimum point of the graph. 5 71 (4 , 8 ) c. Does the graph of = 22 - 5 + 12 cross the x-axis? If yes, then find the coordinates of the point of intersection.

No

(6 Marks)

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4. A curve has an equation = 22 - 11 - 15 d. Write = 22 - 11 - 15 in the form = ( + )2 + .

11 2 241 2 ( - 4 ) - 8

e. Find the coordinates of the minimum point of the graph.

11 241 ( 4 ,- 8 ) f. Does the graph of = 22 - 11 - 15 cross the x-axis? If yes, then find the coordinates of the point of intersection.

(6 Marks)

,

=

11 4

-

241 4

,

=

11 4

+

241 4

5. A curve has an equation = -2 - 5 - 10. Find the coordinates for the maximum point of the graph. 5 15 (- 2 , - 4 )

(5 Marks)

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