Completing the square (AQA GCSE Further Maths): Flashcards

$(x + p)^2 + q$ where $p$ and $q$ are constants

$x^2 - 2px + p^2$

Making coefficients of same powers of $x$ equal on both sides

$x^2 + 2px + p^2$

Expand the brackets on the right side

Start with highest power ($x^2$), then $x$, then constants

Expand all brackets fully

$a(x + b)^2 + c$

Solving quadratic equations and understanding quadratic graphs

Coefficients of the same powers of $x$

$(x + p)^2 + q$

All numbers without $x$