CAIE IGCSE Mathematics Extended E2.2.5 Complete the Square for Expressions in the Form Ax2 Bx C Questions

Practise Extended CAIE IGCSE Mathematics by completing the square, finding missing constants and using the transformed quadratic to identify its turning point or roots.

Exam points

Rewrite ax²+bx+c in completed-square form by halving the x-coefficient and balancing the constant term.
Use completed-square form to identify missing constants or a quadratic turning point, and solve when the evidence asks for roots.

[Maximum number: 2]

$x^2-16x+a$ can be written in the form $(x+b)^2$ .
Find the value of a and the value of b.
$a=\quad b=$

$\begin{aligned}a&=64\\b&=-8\end{aligned}$
B1 for each, or for both $(x-8)^2$ and $x^2-16x+64$

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CAIE IGCSE Mathematics Extended E2.2.5 Complete the Square for Expressions in the Form Ax2 Bx C Questions question 1