CAIE IGCSE Mathematics Extended E2.2.5 Complete the square for expressions in the form ax2 + bx + c

Practise rewriting quadratics by completing the square, finding constants in bracketed forms and using the form to solve equations.

Exam points

write ax^2+bx+c in completed-square form with correct constants
find missing constants when a quadratic is given as a square or transformed square
use completed-square form to solve a quadratic equation

[Maximum number: 2]

Write $x^{2}+10 x+14$ in the form $(x+a)^{2}+b$ .

$(x+5)^2-11$
M1 for $(x+5)^2+k$ , or $(x+\text{their }5)^2+14-(\text{their }5)^2$ , or a=5.

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