What to create	Quiz
Which subject	Mathematics
What age group	Year or Grade 11
What topic	Completing the square
Question types	Open-ended
Number of questions	5
Number of answers	5
Correct answers	Exactly 1
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Year 11 Mathematics Quiz: Completing the Square

Instructions

Complete the following questions on Completing the Square. Each question should be answered in full.

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1. Question 1:
   Given the quadratic expression ( x^2 + 6x + 8 ), convert it into its completed square form.

2. Question 2:
   For the quadratic equation ( 2x^2 - 8x + 3 = 0 ), complete the square to rewrite the equation in the form ( a(x - h)^2 + k = 0 ).

3. Question 3:
   Explain why completing the square is particularly useful for finding the vertex of a quadratic function.

4. Question 4:
   Convert the quadratic expression ( -x^2 + 4x + 5 ) into its completed square form. Provide a detailed explanation of your steps.

5. Question 5:
   Given the function ( f(x) = x^2 + 4x - 12 ), complete the square to express the function in vertex form and state the coordinates of the vertex.

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Answers Key

While the quiz must be answered open-ended, the following information can help guide your responses to ensure accuracy:

1. Possible answer format: ( (x + 3)^2 - 1 )
2. Possible answer format: ( 2(x - 2)^2 - 5 )
3. Possible explanations: Could involve comments on vertex positioning or ease of graphing.
4. Possible answer format: ( -(x - 2)^2 + 9 )
5. Possible answer format: ( (x + 2)^2 - 16 ) with vertex coordinates ( (-2, -16) )

Remember, only one answer is correct for each question. Good luck!