An engineer in Singapore models the path of a cable on a suspension bridge using the equation h = x² - 8x + 20, where h is the height in metres above the road and x is the horizontal distance in metres from one end. Express h in the form (x - p)² + q.

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Question

An engineer in Singapore models the path of a cable on a suspension bridge using the equation h = x² - 8x + 20, where h is the height in metres above the road and x is the horizontal distance in metres from one end. Express h in the form (x - p)² + q.

Accepted Answer

(x - 4)² + 4 — Award 1 mark for completing the square: x² - 8x + 20 = (x - 4)² - 16 + 20 = (x - 4)² + 4. B is incorrect — p should be half of the coefficient of x. C has wrong sign for p. D is incorrect due to arithmetic error in calculating q.

Answer

(x - 8)² + 4

Answer

(x - 4)² + 12

Answer

(x + 4)² + 4

Answer

(x - 4)² + 4

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