3.38: Completing the square and a quadratic inequality

0606/13/M/J/23 — Question 2 · 7 marks

(a)
Write x2+2x+5x^{2} + 2x + 5 in the form (x+a)2+b(x + a)^{2} + b, where aa and bb are rational numbers.
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(b)
Hence write down the coordinates of the stationary point on the curve y=x2+2x+5y = x^{2} + 2x + 5.
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(c)
Solve the inequality x2+2x+5⩾158x^{2} + 2x + 5 \geqslant \dfrac{15}{8}.
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