0580/23 Oct/Nov 2025, Question 14: Quadratic Graphs and the Parabola
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 2 marks
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The question, in short
A quadratic curve has its lowest point at (−3, −5). Give the vertical mirror line and express the curve as y = (x + a)² + b.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 1 mark
State the x-value of the vertical line that splits the curve into matching halves.
- 1The line of symmetry passes through the minimum point (−3, −5)
- 2x = −3
Answerx = −3
Part (b) · 1 mark
Using the turning point, give the completed-square equation with values for a and b.
- 1Minimum at (−a, b) = (−3, −5), so a = 3 and b = −5
- 2y = (x + 3)² − 5
Answer(x + 3)² − 5
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