Question

Find the maximum value of a polynomial -x^2+3x-4

Answer 1

$Let \: Quadratic \: polynomial : \\f(x) = -x^{2}+3x-4$

$Compare \:f(x) \: with \: ax^{2} + bx + c \\we \:get$

$a = -1 , b = 3 \:and \: -4$

$i) \frac{-b}{2a} \\= \frac{-3}{2\times (-1) } \\= \frac{-3}{-2} \\= \frac{3}{2}$

$\red{ Maximum \:value } \\= f\Big(\frac{3}{2}\Big) \\= - \Big(\frac{3}{2}\Big)^{2} + 3 \Big(\frac{3}{2}\Big)- 4 \\= - \frac{9}{4} + \frac{9}{2} - 4 \\= \frac{ -9 + 18 -16}{4} \\= \frac{ 18 - 25}{4} \\= \frac{-7}{4}$

Therefore.,

$\red{ Maximum \:value \: of \: the \: polynomial} \\\green{= \frac{-7}{4}}$

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