Free Grade 3 Working with Quadratic Graphs Flashcards
Free Grade 3 flashcards for Working with Quadratic Graphs: 12 real questions with a full answer key and worked solutions. A quadratic has an x² term. Factorise by finding two numbers that multiply to the constant and add to the x-coefficient; each bracket gives a solution.
Free
Higher
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with quadratic graphs
Explain working with quadratic graphs accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with quadratic graphs
Calculate working with quadratic graphs accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with quadratic graphs
Compare working with quadratic graphs accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with quadratic graphs
Justify working with quadratic graphs accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Quadratic Graphs works
A quadratic has an x² term. Factorise by finding two numbers that multiply to the constant and add to the x-coefficient; each bracket gives a solution.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Factorise x² + 5x + 6.[1]
- 2.Factorise x² − 3x − 18.[1]
- 3.Factorise x² + 1x − 20.[1]
- 4.Factorise x² + 7x − 18.[1]
- 5.Solve x² − 12x + 35 = 0.[2]
- 6.Solve x² + 8x + 12 = 0.[2]
- 7.Solve x² + 4x + 4 = 0.[2]
- 8.Solve x² + 15x + 56 = 0.[2]
- 9.Solve x² − 7x + 6 = 0.[3]
- 10.Solve x² + 0x − 81 = 0.[3]
- 11.Solve x² + 2x − 15 = 0.[3]
- 12.Solve x² + 9x + 18 = 0.[3]
Show answers and working
1. (x + 2)(x + 3)
Find two numbers that multiply to 6 and add to 5: 2 and 3. So x² + 5x + 6 = (x + 2)(x + 3).
2. (x + 3)(x − 6)
Find two numbers that multiply to -18 and add to -3: 3 and -6. So x² − 3x − 18 = (x + 3)(x − 6).
3. (x + 5)(x − 4)
Find two numbers that multiply to -20 and add to 1: 5 and -4. So x² + 1x − 20 = (x + 5)(x − 4).
4. (x − 2)(x + 9)
Find two numbers that multiply to -18 and add to 7: -2 and 9. So x² + 7x − 18 = (x − 2)(x + 9).
5. x = 5 or x = 7
Factorise: (x − 5)(x − 7) = 0. One bracket must be zero: x = 5 or x = 7.
6. x = -6 or x = -2
Factorise: (x + 6)(x + 2) = 0. One bracket must be zero: x = -6 or x = -2.
7. x = -2 or x = -2
Factorise: (x + 2)(x + 2) = 0. One bracket must be zero: x = -2 or x = -2.
8. x = -7 or x = -8
Factorise: (x + 7)(x + 8) = 0. One bracket must be zero: x = -7 or x = -8.
9. x = 1 or x = 6
Factorise: (x − 1)(x − 6) = 0. One bracket must be zero: x = 1 or x = 6.
10. x = 9 or x = -9
Factorise: (x − 9)(x + 9) = 0. One bracket must be zero: x = 9 or x = -9.
11. x = -5 or x = 3
Factorise: (x + 5)(x − 3) = 0. One bracket must be zero: x = -5 or x = 3.
12. x = -6 or x = -3
Factorise: (x + 6)(x + 3) = 0. One bracket must be zero: x = -6 or x = -3.
Worked examples
Factorise x² + 7x + 6.
- Find two numbers that multiply to 6 and add to 7: 1 and 6.
- So x² + 7x + 6 = (x + 1)(x + 6).
- Answer: (x + 1)(x + 6)
Solve x² − 11x + 24 = 0.
- Factorise: (x − 8)(x − 3) = 0.
- One bracket must be zero: x = 8 or x = 3.
- Answer: x = 8 or x = 3
Solve x² + 4x − 45 = 0.
- Factorise: (x + 9)(x − 5) = 0.
- One bracket must be zero: x = -9 or x = 5.
- Answer: x = -9 or x = 5
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Gives x = 3 from (x + 3) = 0.
Correction: x + 3 = 0 means x = −3.
Gets the signs muddled when factorising.
Correction: Check by expanding the brackets.
Teacher tips
- · Use a product–sum grid for finding the pair.
Parent tips
- · Ask what two numbers multiply to 12 and add to 7.
Real-life applications
- · Projectile paths, maximising area.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Working with Quadratic Graphs flashcards really free?
- Yes. Every flashcards on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Introducing Quadratic Graphs, The Quadratic Formula. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Quadratic Graphs?
- Move on to Quadratic Graphs in Context, Expanding Double Brackets, Factorising Quadratics, Completing the Square, which build directly on this idea.
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