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, Prior Knowledge Check
1) Factorise these quadratic 3) Copy and complete the table below
expressions: and use it to plot the graph of
𝑦 = 𝑥3 + 𝑥 − 2
a) 𝑥 2 + 6𝑥 + 5 b) 𝑥 2 − 4𝑥 + 3
(𝑥 + 5)(𝑥 + 1) (𝑥 − 3)(𝑥 − 1) 𝒙 −𝟏. 𝟓 −𝟏 −𝟎. 𝟓 𝟎 𝟎. 𝟓 𝟏 𝟏. 𝟓
𝒚 −𝟔. 𝟖𝟕𝟓 −𝟒 −𝟐. 𝟔𝟐𝟓 −𝟐 −𝟏. 𝟑𝟕𝟓 𝟎 𝟐. 𝟖𝟕𝟓
2) Sketch the graphs of the following
functions:
a) 𝑦 = 𝑥 + 2 𝑥 − 3 b) 𝑦 = 𝑥 2 − 6𝑥 − 7
4) Solve each pair of simultaneous
equations:
−𝟐 𝟑 −𝟏 𝟕 a) 𝑦 = 2𝑥
−𝟕 𝒙 = 𝟐, 𝒚 = 𝟒
𝑥+𝑦 =6
−𝟔
(𝟎. 𝟓, −𝟔. 𝟐𝟓) (𝟑, −𝟏𝟔) b) 𝑦 = 𝑥2
𝒙 = 𝟏, 𝒚 = 𝟏
𝑦 = 2𝑥 − 1
,
, Graphs and Transformations
Cubic graphs are of the form
𝒇 𝒙 = 𝒂𝒙𝟑 + 𝒃𝒙𝟐 + 𝒄𝒙 + 𝒅 = 𝟎,
where 𝒂, 𝒃, 𝒄 and 𝒅 are real
numbers and 𝒂 ≠ 𝟎.
𝑓 𝑥 = 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑 = 0
If 𝑎 is positive If 𝑎 is negative
y y
x x
4A
www.mathsfreeresourcelibrary.com
, Prior Knowledge Check
1) Factorise these quadratic 3) Copy and complete the table below
expressions: and use it to plot the graph of
𝑦 = 𝑥3 + 𝑥 − 2
a) 𝑥 2 + 6𝑥 + 5 b) 𝑥 2 − 4𝑥 + 3
(𝑥 + 5)(𝑥 + 1) (𝑥 − 3)(𝑥 − 1) 𝒙 −𝟏. 𝟓 −𝟏 −𝟎. 𝟓 𝟎 𝟎. 𝟓 𝟏 𝟏. 𝟓
𝒚 −𝟔. 𝟖𝟕𝟓 −𝟒 −𝟐. 𝟔𝟐𝟓 −𝟐 −𝟏. 𝟑𝟕𝟓 𝟎 𝟐. 𝟖𝟕𝟓
2) Sketch the graphs of the following
functions:
a) 𝑦 = 𝑥 + 2 𝑥 − 3 b) 𝑦 = 𝑥 2 − 6𝑥 − 7
4) Solve each pair of simultaneous
equations:
−𝟐 𝟑 −𝟏 𝟕 a) 𝑦 = 2𝑥
−𝟕 𝒙 = 𝟐, 𝒚 = 𝟒
𝑥+𝑦 =6
−𝟔
(𝟎. 𝟓, −𝟔. 𝟐𝟓) (𝟑, −𝟏𝟔) b) 𝑦 = 𝑥2
𝒙 = 𝟏, 𝒚 = 𝟏
𝑦 = 2𝑥 − 1
,
, Graphs and Transformations
Cubic graphs are of the form
𝒇 𝒙 = 𝒂𝒙𝟑 + 𝒃𝒙𝟐 + 𝒄𝒙 + 𝒅 = 𝟎,
where 𝒂, 𝒃, 𝒄 and 𝒅 are real
numbers and 𝒂 ≠ 𝟎.
𝑓 𝑥 = 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑 = 0
If 𝑎 is positive If 𝑎 is negative
y y
x x
4A
