CAIE IGCSE Additional Math 2.1 Find Maximum and Minimum Values Questions

Practise Cambridge IGCSE Additional Mathematics by completing the square or differentiating quadratics to find stationary points and extremal values.

Exam points

Find maximum or minimum values of quadratic functions by completing the square or using differentiation.
Rewrite quadratics in vertex form and identify the stationary point and extremal value accurately.
Report the maximum or minimum value together with the corresponding input where required.

[Maximum number: 4]

(a)

Show that $2 x^{2}+5 x+3$ can be written in the form $2(x+a)^{2}+b$ , where a and b are constants to be found.

[ 2 ]

$2\left(x+\frac{5}{4}\right)^{2}-\frac{1}{8}$ B1 for $2\left(x+\frac{5}{4}\right)^{2}$

B1 for $-\frac{1}{8}$

(b)

Hence write down the coordinates of the stationary point on the curve $y=2 x^{2}+5 x+3$ .

[ 2 ]

$\left(-\frac{5}{4},-\frac{1}{8}\right)$ 2 B1FT on their - a

B1FT on their b

B0 if calculus used as question says ‘Hence’

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