Free Grade 3 Quadratic Graphs in Context Flashcards
Free Grade 3 flashcards for Quadratic Graphs in Context: 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
Core
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify quadratic graphs in context
Identify quadratic graphs in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain quadratic graphs in context
Explain quadratic graphs in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate quadratic graphs in context
Calculate quadratic graphs in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare quadratic graphs in context
Compare quadratic graphs in context 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 Quadratic Graphs in Context 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 + 8x − 9.[1]
- 2.Factorise x² + 0x − 64.[1]
- 3.Factorise x² + 3x + 2.[1]
- 4.Factorise x² − 12x + 27.[1]
- 5.Solve x² − 2x − 63 = 0.[2]
- 6.Solve x² + 4x − 21 = 0.[2]
- 7.Solve x² + 0x − 1 = 0.[2]
- 8.Solve x² − 2x + 1 = 0.[2]
- 9.Solve x² + 4x + 3 = 0.[3]
- 10.Solve x² + 7x + 6 = 0.[3]
- 11.Solve x² − 15x + 56 = 0.[3]
- 12.Solve x² + 2x − 15 = 0.[3]
Show answers and working
1. (x − 1)(x + 9)
Find two numbers that multiply to -9 and add to 8: -1 and 9. So x² + 8x − 9 = (x − 1)(x + 9).
2. (x + 8)(x − 8)
Find two numbers that multiply to -64 and add to 0: 8 and -8. So x² + 0x − 64 = (x + 8)(x − 8).
3. (x + 2)(x + 1)
Find two numbers that multiply to 2 and add to 3: 2 and 1. So x² + 3x + 2 = (x + 2)(x + 1).
4. (x − 3)(x − 9)
Find two numbers that multiply to 27 and add to -12: -3 and -9. So x² − 12x + 27 = (x − 3)(x − 9).
5. x = -7 or x = 9
Factorise: (x + 7)(x − 9) = 0. One bracket must be zero: x = -7 or x = 9.
6. x = -7 or x = 3
Factorise: (x + 7)(x − 3) = 0. One bracket must be zero: x = -7 or x = 3.
7. x = 1 or x = -1
Factorise: (x − 1)(x + 1) = 0. One bracket must be zero: x = 1 or x = -1.
8. x = 1 or x = 1
Factorise: (x − 1)(x − 1) = 0. One bracket must be zero: x = 1 or x = 1.
9. x = -1 or x = -3
Factorise: (x + 1)(x + 3) = 0. One bracket must be zero: x = -1 or x = -3.
10. x = -6 or x = -1
Factorise: (x + 6)(x + 1) = 0. One bracket must be zero: x = -6 or x = -1.
11. x = 8 or x = 7
Factorise: (x − 8)(x − 7) = 0. One bracket must be zero: x = 8 or x = 7.
12. x = 3 or x = -5
Factorise: (x − 3)(x + 5) = 0. One bracket must be zero: x = 3 or x = -5.
Worked examples
Factorise x² − 5x − 24.
- Find two numbers that multiply to -24 and add to -5: -8 and 3.
- So x² − 5x − 24 = (x − 8)(x + 3).
- Answer: (x − 8)(x + 3)
Solve x² − 6x − 7 = 0.
- Factorise: (x + 1)(x − 7) = 0.
- One bracket must be zero: x = -1 or x = 7.
- Answer: x = -1 or x = 7
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
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 Quadratic Graphs in Context 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 Working with Quadratic Graphs, 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 Quadratic Graphs in Context?
- Move on to Expanding Double Brackets, Factorising Quadratics, Completing the Square, The Quadratic Formula, which build directly on this idea.
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