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Drawing quadratic graphs

Free Printable Drawing quadratic graphs PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free drawing quadratic graphs worksheets (PDF), GCSE maths past paper questions and worked solutions for Drawing quadratic graphs (5J). This is a Grade 5 algebra topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Made Easy, Naiker Maths, 1st Class Maths, Dr Austin, Metatutor, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our drawing quadratic graphs revision notes and worked examples with diagrams, try real GCSE past paper drawing quadratic graphs questions with step-by-step solutions, or download a PDF of all drawing quadratic graphs worksheet links.

Free Drawing quadratic graphs PDF Worksheets & Answers

Grade 5 • Topic 5J
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Grade 5 topics
5A - Combining ratios5B - Direct and inverse proportion
5C - Reverse percentages5D - Standard form
5E - Speed5F - Changing the subject
5G - Quadratic expressions5H - Solving quadratic equations
5J - Drawing quadratic graphs5K - Cubic/reciprocal graphs
5L - Simultaneous equations5M - Sector areas and arc lengths
5N - Sim. equ. graphically5P - Midpoint of a line segment
5Q - Gradient of a line5R - Equation of a line
5S - Spheres and cones5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)5V - Exact trig. values
5W - Probability trees5X - Vectors
5Y - Venn diagrams5Z - Density
5AA - Pressure
GCSE Maths Grade 5 Revision Notes & Method

Guide to Drawing quadratic graphs: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

A quadratic graph y = ax2 + bx + c is a smooth, symmetrical U-shaped curve called a parabola (or ∩-shaped if a is negative). When substituting negative values into x2, always use brackets: squaring a negative number gives a positive answer, e.g. (−2)2 = +4.

Plot each (x, y) point from your table and join them with a single smooth curve (never connect points with straight ruler lines). The bottom of the curve is the minimum turning point, and the points where it crosses the x-axis (y = 0) are the roots.

Example 1: Complete the table for y = x2 − 2x − 3.

Solution:

x−2−101234
y50−3−4−305
For x = −2: (−2)2 − 2(−2) − 3 = 4 + 4 − 3 = 5
Notice the symmetrical y-values around (1, −4).

Example 2: From the graph of y = x2 − 2x − 3, find (a) the turning point and (b) the roots of x2 − 2x − 3 = 0.

Solution:

(a) Minimum point on curve: (1, −4)
(b) Crosses y = 0 at x = −1 and 3
Ans: (1, −4); x = −1, 3
x y (−1,0) (3,0) (1,−4)
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Drawing quadratic graphs Questions & Answers

Past Paper Example 1 GCSE May 2025 1F Q21 / 1H Q3 5 marks
Full Paper (PDF) • Mark Scheme (PDF)
y = x² + x – 4
(a) Complete the table of values for x from –3 to 2. (2)
(b) Draw the graph on the grid. (2)
(c) Write down the coordinates of the turning point of the graph. (1)
(a) Complete the table of values for y = x2 + x - 4
@@TABULAR0@@ [2 marks]
(b) On the grid, draw the graph of y = x2 + x - 4 for values of x from –3 to 2 [2 marks]
xyO–3–2–112–5–4–3–2–1123
(c) Write down the coordinates of the turning point of the graph of y = x2 + x - 4 [1 mark]
Worked Solution & Mark Scheme (5 marks)
Part (a) Solution:
x = –2: 4 – 2 – 4 = –2 M1
x = 0: –4
x = 1: 1 + 1 – 4 = –2
x = 2: 4 + 2 – 4 = 2 A1
Answer (a): (2), –2, (–4), –4, –2, 2
Part (b) Solution:
Graph drawn M1 A1
xyO–3–2–112–5–4–3–2–1123
Answer (b): Graph drawn
Part (c) Solution:
Turning point is at x = –0.5, y = (–0.5)² + (–0.5) – 4 = 0.25 – 0.5 – 4 = –4.25 B1
Answer (c): (–0.5, –4.25)
Past Paper Example 2 AQA Nov 2020 2F Q22 / 2H Q7 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
Here is the graph of y = x2 - 7x + 10 for values of x from 0 to 7
0xy1234567–4–2246810
(a) Write down the roots of x2 - 7x + 10 = 0 [2 marks]
(b) Write down the x-coordinate of the turning point of the curve. [1 mark]
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
The roots occur where the curve crosses the x-axis: x = 2 and x = 5. M1 A1
Answer (a): Answer x = 2 and x = 5
Part (b) Solution:
The line of symmetry of the parabola is halfway between the roots: x = 2 + 52 = 3.5. B1
Answer (b): Answer 3.5
Past Paper Example 3 GCSE Jun 2023 3F Q26 / 3H Q7 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
Here is the graph of y = x2 - 2x - 2
xy–2–11234–4–3–2–11234O
(a) Write down the coordinates of the turning point on the graph of y = x2 - 2x - 2 [1 mark]
(b) Write down an estimate for one of the roots of x2 - 2x - 2 = 0 [1 mark]
Worked Solution & Mark Scheme (2 marks)
Part (a) Solution:
Minimum at (1, –3) B1
Answer (a): (1, –3)
Part (b) Solution:
x-intercepts at x ≈ –0.7 and x ≈ 2.7 B1
Answer (b): –0.7 or 2.7

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