Practice Example 2: Completing The Square (4.2) - Quadratic Functions - IB 10 Mathematics

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6 sample questions

Question 1.
Write x² + 6x + 9 as a perfect square.
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Half of 6 is 3, and 3² = 9.
Question 2.
What number must be added to x² − 10x to complete the square? Write the result as a square.
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Halve the coefficient of x, then square it.
3Question 3.
What number must be added to x² + 4x to complete the square?
- 2
- 4
- 8
- 16
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Halve the coefficient of x, then square it.
4Question 4.
Which expression equals x² + 4x + 1?
- (x + 2)² − 3
- (x + 2)² + 1
- (x + 4)² − 15
- (x − 2)² − 3
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Expand each option and compare.
Question 5.
Solve x² + 5x + 2 = 0 by completing the square, giving exact answers.
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An odd coefficient gives fractions; keep them exact until the end.
Question 6.
Find the minimum value of y = 3x² − 12x + 5 and the value of x where it occurs.
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Take out the factor 3 from the x² and x terms only, then complete the square inside the bracket.

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