CAIE IGCSE Mathematics Extended E2.11 Sketching Curves Topic Practice

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Covered syllabus points

E2.11.1 Recognise, sketch and interpret graphs of the following functions: (a)

Question 1

[Maximum number: 3]
Figure for Question 1 — CAIE IGCSE Mathematics Extended
f(x)=x(x+2)(x−3)\mathrm{f}(x)=x(x+2)(x-3)

On the diagram, sketch the graph of y=f(x) for −3⩽x⩽4-3 \leqslant x \leqslant 4. Show the values of the intersections with the axes.

Question 2

[Maximum number: 2]

The minimum point on a quadratic curve is (-3,-5).

Question (a)

(a)

Find the equation of the line of symmetry of the curve.

[ 1 ]

Question (b)

(b)

Write the equation of the curve in the form y=(x+a)2+by=(x+a)^{2}+b.
y=

[ 1 ]

Question 3

[Maximum number: 4]

Find the coordinates of the turning point on the graph of y=7−2x−x2y=7-2x-x^2.

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