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Edexcel IGCSE Maths (4MA1) · Unit 4: Graphs & Functions

IGCSE Maths Quadratic and Cubic Graphs Questions and Answers

Quadratic and Cubic Graphs questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 6 worked examples first, then cover each solution and redo it yourself.

Practise quadratic and cubic graphs in Unit 4 →Quadratic and Cubic Graphs revision notes

What this topic covers

Quadratic and Cubic Graphs worked examples

Worked example 1: Quadratic table of values

Complete a table of values for \(y=x^2-2x-3\) for \(x=-1\) to \(3\).

Solution

  1. \(x=-1\): \(1+2-3=0\).
  2. \(x=0\): \(-3\); \(x=1\): \(-4\); \(x=2\): \(-3\); \(x=3\): \(0\).
  3. The values are symmetrical about \(x=1\).

Answer: 0, −3, −4, −3, 0

Tip: Join the points with a smooth curve, not straight lines.

Worked example 2: Cubic table of values

Find \(y\) on \(y=x^3-x\) for \(x=-2,\ -1,\ 0,\ 1,\ 2\).

Solution

  1. \(x=-2\): \(-8+2=-6\).
  2. \(x=-1,\ 0,\ 1\): \(y=0\).
  3. \(x=2\): \(8-2=6\).

Answer: −6, 0, 0, 0, 6

Tip: Cube negative numbers carefully: \((-2)^3=-8\).

Worked example 3: Reciprocal graph

For \(y=\dfrac{12}{x}\), find \(y\) when \(x=1,2,3,4\) and state the asymptotes.

Solution

  1. \(12,\ 6,\ 4,\ 3\).
  2. The curve never meets the axes: asymptotes \(x=0\) and \(y=0\).

Answer: 12, 6, 4, 3; asymptotes \(x=0\), \(y=0\)

Tip: \(x=0\) is not allowed because you cannot divide by zero.

Worked example 4: Recognising graph shapes

State the type of graph for each equation: (a) \(y=5-2x\) (b) \(y=x^2-4\) (c) \(y=x^3\) (d) \(y=\dfrac{3}{x}\).

Solution

  1. (a) Highest power of \(x\) is 1: straight line with negative gradient.
  2. (b) \(x^2\): U-shaped parabola, minimum at \((0,\ -4)\).
  3. (c) \(x^3\): cubic curve through the origin.
  4. (d) \(\tfrac{1}{x}\) form: reciprocal curve in two parts, asymptotes on the axes.

Answer: (a) linear (b) quadratic (c) cubic (d) reciprocal

Tip: The highest power of x tells you the family of the graph.

Worked example 5: Turning point of a quadratic

Find the turning point of \(y=x^2+6x+1\).

Solution

  1. Complete the square: \((x+3)^2-9+1=(x+3)^2-8\).
  2. Minimum at \((-3,\ -8)\).

Answer: \((-3,\ -8)\)

Tip: The x-coordinate changes sign from the bracket.

Worked example 6: Solving an equation with a graph

The graph of \(y=x^2-3x\) is drawn. Which line should be drawn to solve \(x^2-3x-4=0\), and what are the solutions?

Solution

  1. \(x^2-3x-4=0\) is \(x^2-3x=4\), so draw \(y=4\).
  2. It meets the curve where \(x=-1\) and \(x=4\).

Answer: \(y=4\); \(x=-1,\ 4\)

Tip: Rearrange so one side is the curve already drawn.

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise quadratic and cubic graphs for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test quadratic and cubic graphs?

Either Higher tier paper, 1H or 2H, can test quadratic and cubic graphs: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more quadratic and cubic graphs questions?

In the IGCSE student hub: Unit 4 (Graphs & Functions) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 4 topics: Graphs & Functions