Pearson Edexcel IAL Mathematics P1.1.5 Completing the square

Practise completing the square to rewrite quadratics, locate turning points and support exact equation solving.

Exam points

rewrite ax² + bx + c as a(x + b)² + c and read the minimum or maximum point
use completed-square or factorised forms to solve quadratic equations exactly

[Maximum number: 3]

In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

Figure 2

Figure 2 shows a sketch of the curve C with equation $y=x^{2}-5 x+13$

The point M is the minimum point of C.

The straight line l passes through the origin O and intersects C at the points M and N as shown.

Find, showing your working,

the coordinates of M,

M1 For attempting to complete the square. Look for $(x-2.5)^{2}$
A1 $\quad(x-2.5)^{2}+6.75$ or for correctly extracting x=2.5 as the x coordinate.
A1 $\quad M=(2.5,6.75) \quad$ or $\left(\frac{5}{2}, \frac{27}{4}\right)$

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P1.1.5 - Completing the square question 1