Why does my child think x² + 6x + 2 = (x + 3)² + 2?
Your child leaves the extra square in when completing the square, such as x² + 6x + 2 as (x + 3)² + 2 instead of (x + 3)² - 7.
Why children do it
Halving the 6 to get (x + 3)² is the step children remember. But (x + 3)² is x² + 6x + 9, which has 9 that the expression didn't, so 9 must be taken away: (x + 3)² + 2 − 9 = (x + 3)² − 7. Expanding the answer checks it.
How to help at home
Ask them to expand their answer: (x + 3)² + 2 is x² + 6x + 11, not x² + 6x + 2.
The right way
Write x² + 6x + 11 in the form (x + a)² + b. What are a and b?
- a = 3, b = 2Halve 6: (x + 3)² = x² + 6x + 9, and 11 − 9 = 2.
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