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 ax+by+c=0

2 Cubics using a GDC

3 Exam Question

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

5 More on y=(x-a)²+b

6 Exam Question

7 Axis intercepts

8 Exam Question

9 Exam Question

10 Exam Question

11 Solving ax³+bx²+cx+d=0

12 Plot Quadratics (y=(x-a)²+b)

13 Exam Question

14 Exam Question

15 Investigate 5

16 Min and max

17 Exam Question

18 Exam Question

19 Exam Question

20 Investigate 7

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

22 Exam Question

23 Exam Question

24 Find the gradient

25 O-test 1

26 Plotting O-test 2

27 Timed O-test

28 Exam Question

29 Equations in intercept form

30 Exam Question

31 O-test 2

32 Exam Question

33 O-test 3

34 Straight line recognition 2

35 The vertical wedge

36 Exam Question

37 Exam Question

38 Investigate 3

39 Investigate Quadratic Roots

40 True or false O-test 2

41 Exam Question

42 Exam Question

43 Investigate 2

44 Practise

45 Exam Question

46 Exam Question

47 O-test 2

48 Plot y=mx+c

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

50 Plot Quadratics (y=ax²+bx+c)

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

52 Exam Question

53 Straight line recognition 3

54 O-test 2

55 Exam Question

56 Finding equations

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

58 Exam Question

59 y=ax³+bx²+cx+d

60 Finding perpendicular lines

61 Exam Question

62 O-test 1

63 Exam Question

64 Investigate 4

65 Basic shape

66 Investigate 1

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 Curve recognition

102 Form the cubic

103 Factorising 2

104 Game

105 Match Factors of Quadratic Curves

106 Axis of symmetry

107 Exam Question

108 Curve recognition 3

109 O-test 2

110 Exam Question

111 Linear,quadratic,cubic

112 Perpendicular distance

113 Quadratic curve quiz

114 Game

115 Match Lines (y=mx+c)

116 Example 1

117 Find the equation

118 Straight line recognition

119 Example 1

120 Example 1

121 How to plot them

122 Example 2

123 Example 2

124 Example 2

125 True or false

126 Example 3

127 True or false O-test 1

128 True or false 2

129 Example 3

130 Exam Question

131 Example 3

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 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 O-test 2

171 Plotting 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