Quadratic graphs: GCSE Maths Practice | Revision Workshop
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Quadratic graphs
33 self-marking GCSE practice questions on Quadratic graphs, written specifically for AQA, Pearson, OCR across Foundation and Higher tier. Instant marking with full worked solutions on every question.
A few of the 33 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 4-5
The graph shows the curve y=x2−4x+3. Write down the coordinates of the turning point of the curve.
What are the common mistakes in Quadratic graphs?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Gives only one root of a quadratic equation instead of both
Found one correct crossing point (x=−1) but a quadratic graph usually crosses the x-axis twice - the other crossing point (x=1) also gives a valid solution
Gives the y-intercept instead of the roots when reading key features from a graph
Read off where the curve crosses the
Quick answers about Quadratic graphs
How many Quadratic graphs practice questions are there?
There are 33 self-marking GCSE Maths questions on Quadratic graphs, written for AQA, Pearson, OCR across Foundation and Higher tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Quadratic graphs?
No. You can start practising Quadratic graphs straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
Show the worked solution
The curve is U-shaped (the coefficient of x2 is positive), so the turning point is its lowest point. Reading from the graph, the lowest point is at x=2, y=−1, so the turning point is (2,−1). B1B2
Question 23 marksGrade 6
Here is a table of values for y=x2−x−8:
x: −4,−3,−2,−1,0,1,2,3,4y: 12,4,−2,−6,−8,−8,−6,−2,4
The graph of y=x2−x−8 has been drawn for −4≤x≤4.
(a) Write down the equation of the line of symmetry of the graph.
(b) Use the graph to solve the equation x2−x−8=0. Give your answers to 1 decimal place.
(b)(i) The larger solution.
(b)(ii) The smaller solution.
Show the worked solution
(a) The line of symmetry lies halfway between the roots (or at x=21 from −b/2a): x=0.5
Question 33 marksGrade 8-9
Frankie sketches a quadratic graph that crosses the x-axis at x=−3 and x=5, with the curve dipping down between the roots (a maximum point between them).
Frankie says: "The y-intercept is 15."
(a) Show that what Frankie says could be correct.
(b) Explain why what Frankie says may not be correct.
Assumed that knowing the two roots is enough to determine the WHOLE equation (and therefore a unique y-intercept), without recognising that the equation y=a(x+3)(x−5) has a free parameter a that also affects the y-intercept.
.
B1
(b) Solving x2−x−8=0 with the quadratic formula: x=21±33, giving x≈3.4 or x≈−2.4 (1 d.p.) - matching where the curve crosses the x-axis on the graph. B2 (1 correct answer) B3 (1 correct answer)