The given parabola is:
[tex]y=-3x^2+3x-6[/tex]
It is written in the form:
[tex]y=ax^2+bx+c[/tex]
The axis of symmetry is given by the following formula:
[tex]x=-\frac{b}{2a}[/tex]
Where a=-3 and b=3. Replace these values and solve for x:
[tex]\begin{gathered} x=-\frac{3}{2(-3)}=-\frac{3}{-6}=\frac{3}{6} \\ \text{Divide numerator and denominator by 3 to simplify} \\ x=\frac{3/3}{6/3}=\frac{1}{2} \end{gathered}[/tex]
Therefore, the axis of symmetry is x=1/2
