Edexcel IGCSE 4MA1 Quadratic Graphs: Exam Questions & Answers

Q: How do I find the turning point of a quadratic graph?

Read it off the graph, or complete the square: y = (x + p)² + q has its turning point at (−p, q). It is also halfway between the roots.

Q: What does a cubic graph look like?

y = x³ is an S-shaped curve through the origin. A cubic such as y = x³ − 3x has two turning points; with a negative x³ term the curve falls from left to right instead of rising.

Q: Can I use a calculator for quadratic and cubic graphs in 4MA1?

Yes. A calculator may be used in all four 4MA1 papers, so both Higher papers (1H and 2H) allow one. Most marks are for the method you write down, so show your working.

Q: How long are the 4MA1 Higher papers?

Papers 1H and 2H are 2 hours each and 100 marks each, worth 50% each. Each tier has its own formulae sheet in the exam.

Edexcel IGCSE 4MA1 Quadratic and Cubic Graphs: exam questions and answers, notes and worked examples

Updated October 2026 · By Pete Bromfield

The highest power of

x

tells you the shape:

x^{2}

gives a U-shaped (or upside-down) parabola,

x^{3}

a cubic curve, and

\frac{k}{x}

a reciprocal curve in two parts. Plot from a table of values and join the points with one smooth curve. To solve an equation with a graph you already have, rearrange it so one side is that graph, then read off where the line for the other side crosses it.

Unit 4: Graphs & Functions

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Start with one question on solving quadratic equations. Stuck? Take a hint. No sign-in needed.

Solve

x^{2} - x - 12 = 0

Choose your answer · keys 1–4

x = - 4, x = 3

x = - 12, x = 1

x = - 4, x = - 3

x = - 3, x = 4

Quadratic and Cubic Graphs notes

Tables of values and plotting

Work out $y$ for each $x$ , with brackets round negative values: for $y = x^{2} - 2 x - 3$ , $x = - 2$ gives $4 + 4 - 3 = 5$ . A quadratic's values are symmetrical about its line of symmetry, which is a quick check. Join the points with a smooth curve, not straight lines, and do not flatten the bottom.

Recognising the shapes

$y = a x^{2} + b x + c$ is a ∪ shape when $a > 0$ and a ∩ shape when $a < 0$ . $y = x^{3}$ passes through the origin and rises from left to right; $y = - x^{3}$ falls. $y = \frac{k}{x}$ never meets the axes: the lines $x = 0$ and $y = 0$ are its asymptotes.

Roots, intercepts and turning points

The roots are where the curve crosses the $x$ -axis and the $y$ -intercept is the constant term. $y = x^{2} - 2 x - 3 = (x - 3) (x + 1)$ crosses the $x$ -axis at $x = - 1$ and $x = 3$ , meets the $y$ -axis at $- 3$ and has its minimum point halfway between the roots, at $(1, - 4)$ . A cubic such as $y = x^{3} - 3 x$ can have two turning points, here at $x = - 1$ and $x = 1$ .

Solving equations with a graph

If the graph of $y = x^{2} - 3 x$ is drawn, solve $x^{2} - 3 x - 4 = 0$ by rewriting it as $x^{2} - 3 x = 4$ and drawing the line $y = 4$ . To solve $x^{2} - 3 x = x + 1$ , draw $y = x + 1$ instead. Read the $x$ -values where the line crosses the curve; readings from a graph are estimates, so give them to the accuracy of the graph. The graph shows worked example 3.

Graph of y = x² − 3x and the line y = 4, crossing at (−1, 4) and (4, 4), so x = −1 and x = 4 solve x² − 3x − 4 = 0 — Worked example 3 drawn with our Grapher: the line y = 4 crosses the curve at the two solutions.

Key formulas

Turning point of $y = (x + p)^{2} + q$ Learn it: $(- p, q)$
Quadratic formula, $a x^{2} + b x + c = 0$ On the formula sheet: $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

On the formula sheet = printed on the formulae sheet in the 4MA1 Higher papers, so know where to find it. Learn it = not printed on the 4MA1 Higher formulae sheet, so learn it by heart. The whole 4MA1 formula sheet (free PDF) → · 4MA1 formulas to learn

Quadratic and Cubic Graphs worked examples

Worked example 1: Quadratic table of values

Complete a table of values for $y = x^{2} - 2 x - 3$ for $x = - 1$ to $3$ .

Solution

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

4 steps · 1 to fill in

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

Worked example 2: Turning point of a quadratic

Find the turning point of $y = x^{2} + 6 x + 1$ .

Solution

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

3 steps

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

Worked example 3: Solving an equation with a graph

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

Solution

$x^{2} - 3 x - 4 = 0$ is $x^{2} - 3 x = 4$ , so draw $y = 4$ .
It meets the curve where $x = - 1$ and $x = 4$ .

3 steps · 1 to fill in

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

Play with it Roots and y-intercept: drag the sliders

Change a, p and q so that y = a(x − p)(x − q) crosses the x-axis at −1 and 3 and the y-axis at −6. Then expand your answer into the form y = ax² + bx + c.

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Common quadratic and cubic graphs mistakes

Joining points with straight lines. A quadratic or cubic graph is one smooth curve. Ruled segments between the points are not the graph.
Squaring a negative wrongly. For $x = - 3$ , $x^{2} = 9$ , not $- 9$ . On a calculator type $(- 3)^{2}$ , with the brackets.
A flat bottom. Between two equal lowest values the curve keeps going down to its turning point. Draw through the turning point, not straight across.
Drawing the wrong line. To solve $x^{2} - 3 x - 4 = 0$ from the graph of $y = x^{2} - 3 x$ , draw $y = 4$ , not $y = - 4$ : move the $- 4$ to the other side first.

Where students lose marks across 4MA1, from the examiner reports →

Quadratic and Cubic Graphs FAQ

How do I find the turning point of a quadratic graph?

Read it off the graph, or complete the square: y = (x + p)² + q has its turning point at (−p, q). It is also halfway between the roots.

What does a cubic graph look like?

y = x³ is an S-shaped curve through the origin. A cubic such as y = x³ − 3x has two turning points; with a negative x³ term the curve falls from left to right instead of rising.

Can I use a calculator for quadratic and cubic graphs in 4MA1?

Yes. A calculator may be used in all four 4MA1 papers, so both Higher papers (1H and 2H) allow one. Most marks are for the method you write down, so show your working.

How long are the 4MA1 Higher papers?

Papers 1H and 2H are 2 hours each and 100 marks each, worth 50% each. Each tier has its own formulae sheet in the exam.

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Edexcel IGCSE 4MA1 Quadratic and Cubic Graphs: exam questions and answers, notes and worked examples

Try it first

Quadratic and Cubic Graphs notes

Tables of values and plotting

Recognising the shapes

Roots, intercepts and turning points

Solving equations with a graph

Key formulas

Quadratic and Cubic Graphs worked examples

Worked example 1: Quadratic table of values

Solution

Worked example 2: Turning point of a quadratic

Solution

Worked example 3: Solving an equation with a graph

Solution

Common quadratic and cubic graphs mistakes

Quadratic and Cubic Graphs FAQ

Next steps

Practise quadratic and cubic graphs with your progress saved

More Unit 4 topics: Graphs & Functions