The display shows the graph of

y = (x-a)(x-b)(x-c) , where

a,

b and

c are constants. Graphs like these are called cubic graphs.

Investigate the effect of changing

a,

b and

c.

Make sure that you are clear about these aspects of a cubic graph:

- its basic shape
- its symmetry
- the number of places where the curve crosses the x-axis

More in this topic

1 Points and lines

2 Exam Question

3 Exam Question

4 Find the gradient

5 O-test 1

6 Plotting O-test 2

7 Timed O-test

8 Exam Question

9 Equations in intercept form

10 Exam Question

11 O-test 2

12 Exam Question

13 O-test 3

14 Straight line recognition 2

15 The vertical wedge

16 Exam Question

17 Exam Question

18 Investigate 3

19 Solving problems

20 True or false O-test 2

21 Exam Question

22 Exam Question

23 Investigate 2

24 Practise

25 Exam Question

26 Exam Question

27 O-test 2

28 y=mx+c

29 y=c(x-a)(x-b)

30 y=ax²+bx+c

31 y=(x-a)(x-b)

32 Exam Question

33 Straight line recognition 3

34 O-test 2

35 Exam Question

36 Finding equations

37 y=(x-a)(x-b)(x-c)

38 Exam Question

39 y=ax³+bx²+cx+d

40 Finding perpendicular lines

41 Exam Question

42 O-test 1

43 Exam Question

44 Investigate 4

45 ax+by+c=0

46 Cubics using a GDC

47 Exam Question

48 y-y_{1}=m(x-x_{1})

49 More on y=(x-a)²+b

50 Exam Question

51 Axis intercepts

52 Exam Question

53 Exam Question

54 Exam Question

55 Solving ax³+bx²+cx+d=0

56 y=(x-a)²+b

57 Exam Question

58 Exam Question

59 Investigate 5

60 Min and max

61 Exam Question

62 Exam Question

63 Exam Question

64 Investigate 7

65 Introduction

66 y=mx+c

67 Investigate 1

68 Investigate 1

69 Basic shape

70 Investigate 1

71 Plotting O-test 1

72 Observation O-test 1

73 Investigate 2

74 Investigate 2

75 Observation O-test

76 Plotting O-test 1

77 Investigate 2

78 Plotting O-test 2

79 Investigate 3

80 Investigate 3

81 Timed O-test

82 Observation O-test 2

83 Game

84 Find the equation 1

85 Investigate 4

86 More on y=(x-a)(x-b)

87 Identify the coefficients

88 Using a GDC

89 Find the equation 2

90 Investigate 5

91 Game

92 Observation O-test

93 How to plot them

94 Find the equation

95 Investigate 6

96 O-test 1

97 How to plot them 2

98 How to plot them 1

99 Curve recognition

100 Form the cubic

101 Factorising 2

102 Game

103 How to sketch them

104 Factorising 1

105 Curve recognition 2

106 Axis of symmetry

107 Exam Question

108 Perpendicular distance

109 Curve recognition 3

110 O-test 2

111 Exam Question

112 Linear,quadratic,cubic

113 Game

114 Summary

115 Quadratic curve quiz

116 Example 1

117 How to plot them

118 Example 1

119 Find the equation

120 Straight line recognition

121 Example 1

122 Example 2

123 Example 2

124 Example 2

125 True or false

126 True or false 2

127 Example 3

128 Exam Question

129 Example 3

130 Example 3

131 True or false O-test 1

132 Example 4

133 Example 4

134 Finding equations 2

135 Example 4

136 Example 5

137 O-test 1

138 Example 5

139 Finding equations 3

140 Example 5

141 Example 6

142 Example 6

143 O-test 3

144 Example 7

145 Example 8

146 Example 9

147 Exam Question

148 Exam Question

149 Exam Question

150 Exam Question

151 Exam Question

152 Exam Question

153 Exam Question

154 Exam Question

155 Exam Question

156 Exam Question

157 Exam Question

158 Exam Question

159 Example 1

160 Exam Question

161 Exam Question

162 Example 2

163 Exam Question

164 Example 3

165 Example 4

166 Example 5

167 Plotting O-test 1

168 O-test 1

169 Observation O-test 1

170 Plotting O-test 2

171 O-test 2

172 O-test 3

173 O-test 4

174 O-test 5

175 True or false O-test

176 Finding parallel lines

177 True or false O-test 1

178 O-test 1

179 Finding parallel lines 2

180 O-test 1

181 True or false O-test 2

182 O-test 2

183 Exam Question

184 O-test 2

185 Finding parallel lines 3

186 Exam Question

187 Exam Question

188 Exam Question

189 Exam Question

190 Exam Question

191 Exam Question

192 Exam Question

193 Parallel and perpendicular lines

194 Exam Question

195 Perpendicular gradients

196 Exam Question

197 Exam Question

198 Exam Question

199 Perpendicular gradients 2

200 Right angles

201 Exam Question

202 Finding perpendicular lines 2

203 Exam Question

204 Finding perpendicular lines 3

205 Exam Question

206 Finding perpendicular lines 4

207 Exam Question

208 Exam Question

209 O-test 4

210 Exam Question

211 Exam Question

212 Exam Question

213 Vocabulary O-test

214 Exam Question

215 Exam Question

216 Finding lines - the method

217 Analysis

218 Linear graph quiz

219 Exam O-test

220 True or false

221 True or false 2

222 True or false O-test 1

223 True or false O-test 2

224 Quiz

225 Quiz 2

226 Timed O-test

227 O-test 5

228 O-test 6

229 Exam O-test 1

230 Exam O-test 2

231 Exam O-test 3

232 Exam O-test 4

233 Exam O-test 5

234 Exam O-test 6

235 Exam O-test 7