Answer: The correct option is (C) x = 2.
Step-by-step explanation: We are given to select the correct option that gives the line of symmetry for the graph of the following equation:
\(y=-3x^2+12x-11~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We know that the graph of a quadratic equation in the form
\(y=ax^2+bx+c\) has as its line of symmetry given by:
\(x=-\dfrac{b}{2a}.\)
From equation (i), we have
a = - 3, b = 12 and c = -11.
Therefore, the line of symmetry for the given equation is
\(x=-\dfrac{b}{2a}\\\\\\\Rightarrow x=-\dfrac{12}{2\times (-3)}\\\\\\\Rightarrow x=\dfrac{12}{6}\\\\\\\Rightarrow x=2.\)
Thus, the required line of symmetry is x = 2.
Option (C) is correct.
