Completing the square - in the form
Write a monic quadratic as a squared parenthesis plus or minus a constant.
- Halve the coefficient of
to get the number inside the parenthesis. - Squaring that parenthesis introduces an extra constant. Subtract it, then include the original constant.
- The result has the form
.
Example 1
An even coefficient
Complete the square.
Example 2
An odd coefficient
Write the expression in completed-square form.
Remember
The sign goes inside the parenthesis too: half of
Your turn
5 practice questions0 of 5 answers checked
Question 1
Complete the square.
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Question 2
Complete the square.
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Question 3
Complete the square.
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Question 4
Complete the square.
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Question 5
Complete the square.
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Complete the square.
Complete the square.
Complete the square.
Complete the square.
Complete the square.