A curve is given by \(y = 5 - x - 2x^{2}\). Find the equation of its line of symmetry.

A.

\(x = \frac{-41}{8}\)

B.

\(x = \frac{-1}{4}\)

C.

\(x = \frac{1}{4}\)

D.

\(x = \frac{41}{8}\)

Correct answer is B

The line of symmetry of the curve is at the minimum point of the curve (ie y' = 0)

\(\frac{ \mathrm d}{ \mathrm d x} \left ( 5-x-2x^{2} \right)\) = -1 - 4x

If y' = 0, we have \(-1 - 4x = 0 \implies 4x = -1\)

\(x = \frac{-1}{4}\)