The minimum value of (x - 2)(x - 9) is?

Answer: Option D

$$\begin{array}{rl}& \left(x-2\right)\left(x-9\right)\\ & =x^2-9x-2x+18\\ & =x^2-11x+18\\ & =a{x}^2+bx+c=0\\ & \text{For minimum value}\\ & =\frac{4ac-b^2}{4a}\\ & =\frac{4\times 1\times 18-{\left(-11\right)}^2}{4\times 1}\\ & =\frac{72-121}{4}\\ & =\frac{-49}{4}\\ & =-\frac{49}{4}\end{array}$$