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Focus of parabola $y = a x^{2} + b x + c$ is

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$(\frac{- b}{2 a}, \frac{b^{2} - 4 a c + 1}{4 a})$

$(\frac{- b}{2 a}, \frac{4 a c - b^{2} + 1}{4 a})$

$(\frac{- b}{2 a}, \frac{b^{2} - 4 a c - 1}{4 a})$

$(\frac{b}{2 a}, \frac{b^{2} + 4 a c + 1}{4 a})$

answer is B.

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Detailed Solution

$y = a x^{2} + b x + c$

Add and substract ${(\frac{b}{2 a})}^{2}$

${(x - (- \frac{b}{2 a}))}^{2} = \frac{1}{a} (y - \frac{4 a c - b^{2}}{4 a})$

$(h . k) = (\frac{- b}{2 a}, \frac{4 a c - b^{2}}{4 a})$

$s = (h, k + a)$

$(\frac{- b}{2 a}, \frac{4 a c - b^{2}}{4 a} + \frac{1}{4 a})$

$(\frac{- b}{2 a}, \frac{4 a c - b^{2} + 1}{4 a})$

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