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 Exam Question

2 Investigate 3

3 Straight line recognition 2

4 The vertical wedge

5 Exam Question

6 True or false O-test 2

7 Exam Question

8 Exam Question

9 Investigate 2

10 Investigate Quadratic Roots

11 Exam Question

12 Exam Question

13 O-test 2

14 Practise

15 Plot y=mx+c

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

17 O-test 2

18 Exam Question

19 Plot Quadratics (y=ax²+bx+c)

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

21 Exam Question

22 Straight line recognition 3

23 Exam Question

24 Finding equations

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

26 Exam Question

27 O-test 1

28 Exam Question

29 Investigate 4

30 y=ax³+bx²+cx+d

31 Finding perpendicular lines

32 Exam Question

33 ax+by+c=0

34 Cubics using a GDC

35 Exam Question

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

37 More on y=(x-a)²+b

38 Exam Question

39 Axis intercepts

40 Exam Question

41 Exam Question

42 Exam Question

43 Exam Question

44 Investigate 5

45 Solving ax³+bx²+cx+d=0

46 Plot Quadratics (y=(x-a)²+b)

47 Exam Question

48 Exam Question

49 Exam Question

50 Investigate 7

51 Min and max

52 Exam Question

53 Find the gradient

54 O-test 1

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

56 Exam Question

57 Plotting O-test 2

58 Timed O-test

59 Exam Question

60 O-test 2

61 Exam Question

62 O-test 3

63 Exam Question

64 Equations in intercept form

65 y=mx+c

66 Investigate 1

67 Investigate 1

68 Investigate 1

69 Basic shape

70 Introduction

71 Investigate 2

72 Observation O-test

73 Plotting O-test 1

74 Investigate 2

75 Plotting O-test 1

76 Observation 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 Identify the coefficients

85 Using a GDC

86 Find the equation 1

87 Investigate 4

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

89 Investigate 5

90 Game

91 Observation O-test

92 Find the equation 2

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 How to sketch them

100 Factorising 1

101 Curve recognition

102 Form the cubic

103 Game

104 Factorising 2

105 Match Factors of Quadratic Curves

106 Axis of symmetry

107 Exam Question

108 Perpendicular distance

109 O-test 2

110 Curve recognition 3

111 Exam Question

112 Linear,quadratic,cubic

113 Game

114 Match Lines (y=mx+c)

115 Quadratic curve quiz

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 True or false

125 Example 2

126 Exam Question

127 Example 3

128 Example 3

129 True or false O-test 1

130 Example 3

131 True or false 2

132 Example 4

133 Example 4

134 Example 4

135 Finding equations 2

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 Exam Question

183 O-test 2

184 Finding parallel lines 3

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 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 Exam Question

210 O-test 4

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 Timed O-test

226 Quiz 2

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