CAIE IGCSE Additional Math 2.1 maximum and minimum values

Use this quadratic extrema page to rewrite quadratics in completed-square form and read the stationary point or minimum value.

Exam points

Rewrite quadratics in completed-square form to identify the stationary point.
Read the minimum or maximum value from the completed-square expression.
Use vertex coordinates to support a sketch or range statement when required.

[Maximum number: 3]

(a) Find the coordinates of the stationary point on the curve y=(x+3)(x-4).

Find the coordinates of the stationary point on the curve y=(x+3)(x-4).

$\begin{aligned} y=x^{2}-x-12 \frac{\mathrm{~d} y}{\mathrm{~d} x}=2 x-1 \text { or }(x+3)+(x-4) \text { or } y=\left(x-\frac{1}{2}\right)^{2}-\frac{49}{4} \text { or using symmetry } x=\frac{4-3}{2} \end{aligned}$

M1

For expanding the brackets and
differentiate with at least one correct term
or for using the product rule
or for completing the square
or for using symmetry

$x=\frac{1}{2}$

A1

$y=-\frac{49}{4}$ oe

A1

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2.1. Find maximum and minimum values question 1