First, you need to put the equation of this quadratic into standard form.
y + 3x - 6 = -3(x - 2)² + 4
y = -3(x - 2)² + 4 - 3x + 6
y = -3(x²- 4x + 4) + 4 - 3x +6
y = -3x² + 12x - 12 - 3x + 10
y = -3x² + 8x - 2
now from this standard form, the equation of the axis of symmetry will be defined as [tex]x = \frac{-b}{2a} [/tex]
Note from standard equation above, b = 8 and a = -3
[tex]x = \frac{-8}{2(-3)} [/tex]
x = [tex] \frac{4}{3} [/tex] and this is our equation for the axis of symmetry
