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7 marksCompleting the Square

CSEC Mathematics · January 2004 · Paper 2 · Question 10(c)(i)

Given f(x) = 4x² - 7x + 3.

Write f(x) = 4x² - 7x + 3 in the form f(x) = a(x + b)² + c, where a, b and c are constants.

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  1. 10(c)(ii)a)State the minimum value of f(x).[7 marks]
  2. 10(c)(ii)b)State the value of x for which the minimum occurs.[7 marks]
  3. 10(a)(i)Write TWO inequalities to represent this information.[4 marks]
  4. 10(a)(ii)Write an inequality to represent this information.[4 marks]
  5. 10(b)Using a scale of 1 cm to represent 5 units on each axis, draw a graph of the THREE inequalities and label the region, R, which satisfies ALL of the…[7 marks]
  6. 10(c)(i)Write an expression for the profit, P.[4 marks]
  7. 10(c)(ii)Determine the number of dresses and shirts that Mrs Singh should buy to make the maximum profit.[4 marks]
  8. 10(c)(iii)Calculate the maximum profit.[4 marks]

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