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0606/21 May/Jun 2025, Question 1: Completed Square Form and Turning Points

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 5 marks

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The question, in short

For the curve y = x² + 2x − 3, find the turning point by completing the square, then draw the graph and give where it crosses the axes.

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Part (a) · 3 marks

Rewrite the quadratic in completed-square form and use it to state the coordinates of the stationary point.

  1. 1x² + 2x − 3 = (x + 1)² − 1 − 3
  2. 2= (x + 1)² − 4
  3. 3Minimum when x + 1 = 0
  4. 4Stationary point (−1, −4)

Answer(−1, −4)

Part (b) · 2 marks

Draw the curve on the given axes and write down the x-axis and y-axis crossing values.

  1. 1y = 0: x² + 2x − 3 = (x + 3)(x − 1) = 0, so x = −3 or 1
  2. 2x = 0: y = −3
  3. 3Minimum at (−1, −4), in the 3rd quadrant

AnswerU-shaped parabola with minimum at (−1, −4) in the 3rd quadrant, crossing the x-axis at −3 and 1 and the y-axis at −3

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Also searched as: 0606/21/M/J/25 · 0606_s25_qp_21 · 0606 s25 21 · question 1.
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