The display shows the graph of

y = (x^2+a)(x-b) , where

a and

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

Investigate the effect of changing

a and

b.

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 Finding perpendicular lines

2 Exam Question

3 O-test 1

4 Exam Question

5 Investigate 4

6 y=ax³+bx²+cx+d

7 Cubics using a GDC

8 Exam Question

9 ax+by+c=0

10 Exam Question

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

12 More on y=(x-a)²+b

13 Axis intercepts

14 Exam Question

15 Exam Question

16 Exam Question

17 Plot Quadratics (y=(x-a)²+b)

18 Exam Question

19 Exam Question

20 Investigate 5

21 Solving ax³+bx²+cx+d=0

22 Exam Question

23 Exam Question

24 Exam Question

25 Investigate 7

26 Min and max

27 Exam Question

28 Exam Question

29 Find the gradient

30 O-test 1

31 Match Lines (y=mx+c) to Points

32 Plotting O-test 2

33 Timed O-test

34 Exam Question

35 Equations in intercept form

36 Exam Question

37 O-test 2

38 Exam Question

39 O-test 3

40 The vertical wedge

41 Exam Question

42 Exam Question

43 Investigate 3

44 Straight line recognition 2

45 True or false O-test 2

46 Exam Question

47 Exam Question

48 Investigate 2

49 Investigate Quadratic Roots

50 Exam Question

51 Exam Question

52 O-test 2

53 Practise

54 Plot y=mx+c

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

56 Straight line recognition 3

57 O-test 2

58 Exam Question

59 Plot Quadratics (y=ax²+bx+c)

60 Plot Quadratics (y=(x-a)(x-b))

61 Exam Question

62 Exam Question

63 Finding equations

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

65 Investigate 1

66 Basic shape

67 Introduction

68 y=mx+c

69 Investigate 1

70 Investigate 1

71 Plotting O-test 1

72 Investigate 2

73 Plotting O-test 1

74 Observation O-test 1

75 Investigate 2

76 Investigate 2

77 Observation O-test

78 Investigate 3

79 Investigate 3

80 Timed O-test

81 Observation O-test 2

82 Game

83 Plotting O-test 2

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 Observation O-test

90 Find the equation 2

91 Investigate 5

92 Game

93 O-test 1

94 How to plot them 2

95 How to plot them 1

96 How to plot them

97 Find the equation

98 Investigate 6

99 How to sketch them

100 Factorising 1

101 Form the cubic

102 Curve recognition

103 Game

104 Factorising 2

105 Axis of symmetry

106 Match Factors of Quadratic Curves

107 Exam Question

108 O-test 2

109 Curve recognition 3

110 Exam Question

111 Linear,quadratic,cubic

112 Perpendicular distance

113 Match Lines (y=mx+c)

114 Quadratic curve quiz

115 Game

116 How to plot them

117 Example 1

118 Find the equation

119 Straight line recognition

120 Example 1

121 Example 1

122 Example 2

123 Example 2

124 Example 2

125 True or false

126 Example 3

127 Example 3

128 True or false O-test 1

129 True or false 2

130 Example 3

131 Exam Question

132 Example 4

133 Example 4

134 Finding equations 2

135 Example 4

136 Example 5

137 Example 5

138 O-test 1

139 Example 5

140 Finding equations 3

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 Exam Question

160 Example 1

161 Exam Question

162 Example 2

163 Exam Question

164 Example 3

165 Example 4

166 Example 5

167 O-test 1

168 Observation O-test 1

169 Plotting 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 True or false O-test 1

177 Finding parallel lines

178 O-test 1

179 True or false O-test 2

180 O-test 1

181 Finding parallel lines 2

182 Finding parallel lines 3

183 O-test 2

184 Exam Question

185 O-test 2

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 Perpendicular gradients

195 Exam Question

196 Exam Question

197 Exam Question

198 Perpendicular gradients 2

199 Exam Question

200 Exam Question

201 Right angles

202 Exam Question

203 Finding perpendicular lines 2

204 Finding perpendicular lines 3

205 Exam Question

206 Finding perpendicular lines 4

207 Exam Question

208 Exam Question

209 Exam Question

210 O-test 4

211 Exam Question

212 Exam Question

213 Exam Question

214 Vocabulary O-test

215 Finding lines - the method

216 Exam Question

217 Analysis

218 Linear graph quiz

219 True or false

220 Exam O-test

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