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:
[tex]y=-3x^2+12x-11~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the graph of a quadratic equation in the form
[tex]y=ax^2+bx+c[/tex] has as its line of symmetry given by:
[tex]x=-\dfrac{b}{2a}.[/tex]
From equation (i), we have
a = - 3, b = 12 and c = -11.
Therefore, the line of symmetry for the given equation is
[tex]x=-\dfrac{b}{2a}\\\\\\\Rightarrow x=-\dfrac{12}{2\times (-3)}\\\\\\\Rightarrow x=\dfrac{12}{6}\\\\\\\Rightarrow x=2.[/tex]
Thus, the required line of symmetry is x = 2.
Option (C) is correct.
