3.51: Completing the square and range

0606/21/M/J/24 — Question 2 · 4 marks

(a)
Write 2x2+3x42x^{2} + 3x - 4 in the form a(x+b)2+ca\bigl(x + b\bigr)^{2} + c, where aa, bb and cc are constants.
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(b)
Hence write down the range of f(x)=2x2+3x4f(x) = 2x^{2} + 3x - 4, where xRx \in \mathbb{R}.
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