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O-Level Mathematics
ZIMSEC • Cambridge • GCSE • Other Syllabuses
ZIMSEC • Cambridge • GCSE • Other Syllabuses
QUADRATIC FUNCTIONS
Question
The curve of a quadratic function crosses the x-axis when x = -1. Its line of symmetry has the equation x = 3.
Find the y-coordinate of the turning point. [4]
Solution
x-axis: x = -1
Line of symmetry: x = 3
Algebraic Application
Let x = r be the other root to the right of the line of symmetry.
Equation of line of symmetry:
x = (sum of roots) / 2
3 = (-1 + r) / 2
6 = -1 + r
r = 7
Let the equation of the curve be
y = x² – (sum of roots)x + product of roots
y = x² – (-1 + 7)x + (-1 × 7)
y = x² – 6x – 7
Substitute x = 3 in y = x² – 6x – 7
y = (3)² – 6(3) – 7
y = 9 – 18 – 7
y = -16
Final Answer
y = -16
Therefore, the y-coordinate of the turning point is -16.
Sketch
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