Completing the Square (Edexcel A-Level Mathematics): Flashcards

A squared bracket, e.g., $(x+3)^2$

$x^2 + 6x + 9$

$(x+3)^2 - 9$

$a = \frac{b}{2}$

$(x+6)^2 - 36$

$(x+9)^2 - 84$

Work in fractions: $(x+\frac{3}{2})^2 - \frac{9}{4}$

Factor out 2: $2(x^2 + 6x) - 1$

Factor out -1: $-[x^2 - 10x] - 5$

The turning (max/min) point

$(-3, -19)$

$x = -h$

When $x = -h$ (at line of symmetry)

$y = \frac{7}{4}$ (horizontal line)

$3(x+2)^2 - 5$