Recall · M4U-P1-QP-QUADRATICS-COMPLETING-SQUARE-01
complete square
Maths4U Original · Short practice
Write \(x^2-10x+8=(x-p)^2+q\), where \(p>0\). Enter \(p\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Pure 1 course · All short practice · Notes & examples
Maths4U Original · 9709 Pure 1
Completing the square and range
Check a short answer, use a hint, then study the reasoning. These checks assess the final answer; use the exam-style problems to practise written explanations.
Guest progress stays in this browser. Sign in to save future checked answers to your account.
Method · M4U-P1-QP-QUADRATICS-COMPLETING-SQUARE-02
scaled square
Maths4U Original · Short practice
Find the minimum value of \(2x^2+12x+23\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Apply · M4U-P1-QP-QUADRATICS-COMPLETING-SQUARE-03
negative leading coefficient
Maths4U Original · Short practice
Find the maximum value of \(-3x^2+12x-7\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Check understanding · M4U-P1-QP-QUADRATICS-COMPLETING-SQUARE-04
interpret completed square
Maths4U Original · Short practice
How many real roots does \(4(x-2)^2+7=6\) have?Choose one answer.
Fresh review variant · M4U-P1-QP-VAR-QUADRATICS-COMPLETING-SQUARE-01
complete square
Maths4U Original · Short practice
Write \(x^2-8x+3=(x-p)^2+q\), where \(p>0\). Find \(p\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-QUADRATICS-COMPLETING-SQUARE-02
scaled square
Maths4U Original · Short practice
Find the minimum of \(3x^2+12x+19\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-QUADRATICS-COMPLETING-SQUARE-03
negative leading coefficient
Maths4U Original · Short practice
Find the maximum of \(-2x^2+8x\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-QUADRATICS-COMPLETING-SQUARE-04
interpret completed square
Maths4U Original · Short practice
How many distinct real roots does \(-2(x+3)^2+7=7\) have?Enter one number or fraction. Round decimals to at least six decimal places when needed.