Cambridge Additional Mathematics

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-2 2 x

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Quadratics (Chapter 3) 75

4 For each of the following quadratic equations, find the discriminant¢and hence draw its sign diagram.

Find all values ofkfor which the equation has:

i two distinct real roots ii two real roots iii a repeated root iv no real roots.

a 2 x^2 +kx¡k=0 b kx^2 ¡ 2 x+k=0

c x^2 +(k+2)x+4=0 d 2 x^2 +(k¡2)x+2=0

e x^2 +(3k¡1)x+(2k+ 10) = 0 f (k+1)x^2 +kx+k=0

Aquadratic functionhas the form y=ax^2 +bx+c where a 6 =0.

The simplest quadratic function is y=x^2. Its graph can be

drawn from a table of values.

x ¡ 3 ¡ 2 ¡ 1 0 1 2 3

y 9 4 1 0 1 4 9

The graph of a quadratic function is called aparabola.

The parabola is one of theconic sections, the others being circles, hyperbolae,

and ellipses. They are called conic sections because they can be obtained by

cutting a cone with a plane. A parabola is produced by cutting the cone with a

plane parallel to its slant side.

There are many examples of parabolas in everyday life, including water fountains, suspension bridges, and

radio telescopes.

D Quadratic functions

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_03\075CamAdd_03.cdr Thursday, 19 December 2013 3:46:01 PM GR8GREG