5m6m ()x¡+¡2 mxmxcm4cm()x¡+¡3 cm5cm()x¡-¡2 cm3cmxcm()x¡+¡2 cm3 Use the quadratic formula to solve:a 2 x^2 +2x¡1=0 b1
x¡
1
1 ¡x=2
4 Use technology to solve:
a 7 x^2 +9x¡4=0 b 9 ¡ 2 x^2 =0 c ¡ 2 x+5¡x^2 =0
5 Ifg(x)=x^2 ¡ 3 x¡ 15 find:
a g(0) b g(1) c xsuch thatg(x)=3.6 On the same set of axes, sketchy=x^2 and the function:
a y=3x^2 b y=(x¡2)^2 +1 c y=¡(x+3)^2 ¡ 27 For y=¡2(x¡1)(x+3)find the:
aidirection the parabola opens ii y-intercept
iii x-intercepts iv equation of the line of symmetry.
b Sketch a graph of the function showing all of the above features.8 For y=x^2 ¡ 2 x¡ 15 find the:
aiy-intercept ii x-intercepts
iii equation of the line of symmetry iv coordinates of the vertex.
b Sketch a graph of the function showing all of the above features.9 If the graph of f(x)=x^2 +bx+c has its vertex at (¡ 3 ,¡11), find f(x).10 Given the function f(x)=3(x¡2)^2 ¡ 1 :
a find the coordinates of the vertex b find they-intercept
c sketch the graph of f(x):11 Find the equation of the quadratic function with vertex(¡ 1 ,¡5)andy-intercept¡ 3. Give your
answer in the form f(x)=a(x¡h)^2 +k.12 The graph of a quadratic function hasx-intercepts¡ 4 and¡^13 , and passes through the point
(¡ 1 ,¡18). Find the quadratic function in expanded form.13 Find the quadratic function which has vertex(6,¡2)and passes through the point(4,16). Give
your answer in the form f(x)=ax^2 +bx+c.14 The length of a rectangle is three times its width, and its area is 9 cm^2. Find the dimensions of the
rectangle.
15 In a right angled triangle, the second to longest side is 5 cm longer than the shortest side, and the
hypotenuse is three times longer than the shortest side. Find the exact length of the hypotenuse.
16 Findxin:
abc452 Quadratic equations and functions (Chapter 21)IGCSE01
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Y:\HAESE\IGCSE01\IG01_21\452IGCSE01_21.CDR Monday, 27 October 2008 2:10:23 PM PETER