Grade 11 Maths · Algebra

Use the quadratic formula

Solve a quadratic using x = (−b ± √(b² − 4ac)) ÷ 2a, putting in a, b and c with the right signs and usually rounding to two decimals.

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1) Quadratic formula grade 11 | IntroKevinmathscience

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How To Solve Quadratic Equations Using The Quadratic FormulaThe Organic Chemistry Tutor

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Question 1.1.2 · May/June 2025 · Paper 1 · National (DBE) · 3 marks

1.1 Solve for

x

1.1.2

3 x^{2} + 6 x + 1 = 0

(correct to TWO decimal places)(3)

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More past paper questions: use the quadratic formula

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3. Question 1.1.2 · November 2024 · Paper 1 · National (DBE) · 4 marks
1.1 Solve for $x$ :
1.1.2 $2 x^{2} + 1 = 4 x$ (correct to TWO decimal places)(4)
Show the memo (3 ticks)Memo
1. ✓
  Write in standard form $2 x^{2} - 4 x + 1 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Substitute into quadratic formula $x = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 ( 2 ) ( 1 )}{2 ( 2 )}$
  1 mark · Use the quadratic formula
3. ✓
  Calculate final values $x = 1, 71$ or $x = 0, 29$
  2 marks · Use the quadratic formula
4. Question 1.1.2 · March 2025 · Paper 1 · Provincial · 3 marks
1.1 Solve for $x$ :
1.1.2 $4 x^{2} - x - 2 = 0$ (answer correct to TWO decimal places)(3)
Show the memo (3 ticks)Memo
1. ✓
  Substitute into quadratic formula $x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$
  $x = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 ( 4 ) ( - 2 )}{2 ( 4 )}$
  1 mark · Use the quadratic formula
2. ✓
  First answer $x = 0, 84$
  1 mark · Use the quadratic formula
3. ✓
  Second answer $x = - 0, 59$
  1 mark · Use the quadratic formula
5. Question 2.2.2 · March 2025 · Provincial · 2 marks
Solve for x:
2.2 Given: $3 x^{2} - 5 x - 17 = 0$
2.2.2 Use the quadratic formula to calculate the value(s) of x. (Correct to TWO decimal places).(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution $x = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 ( 3 ) ( - 17 )}{2 ( 3 )}$
  1 mark · Use the quadratic formula
2. ✓
  Final answers $x = 3, 36$ or $x = - 1, 69$
  1 mark · Use the quadratic formula
6. Question 1.4.1 · March 2025 · Provincial · 2 marks
1.4 An equation is given: $\frac{1}{2} x^{2} + m x + 18 = 0$
1.4.1 Solve for $x$ in terms of $m$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Correct substitution into the quadratic formula $x = \frac{- m \pm m ^{2} - 4 ( \frac{1}{2} ) ( 18 )}{2 ( \frac{1}{2} )}$
  1 mark · Use the quadratic formula
2. ✓
  Simplified answer $x = - m \pm m^{2} - 36$
  1 mark · Use the quadratic formula

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