ANSWER
[tex]x =\frac{3}{ 2}[/tex]
EXPLANATION
The given equation is
[tex]y + 3x - 6 = - 3(x - 2)^{2} + 4[/tex]
Expand the parenthesis:
[tex]y + 3x - 6 = - 3( {x}^{2} - 4x + 4) + 4[/tex]
[tex]y + 3x - 6 = - 3 {x}^{2} + 12x + - 12 + 4[/tex]
Write in standard form:
[tex]y = - 3 {x}^{2} + 12x - 3x+ - 12 + 4 + 6[/tex]
[tex]y = - 3 {x}^{2} + 9x-2[/tex]
where
[tex]a=-3,b=9,c=-2[/tex]
The axis of symmetry is given by the formula:
[tex]x = - \frac{b}{2a} [/tex]
Plug the values to get:
[tex]x = - \frac{9}{ 2(- 3)} [/tex]
[tex]x =\frac{3}{ 2}[/tex]
The equation of axis of symmetry is
[tex]x =\frac{3}{ 2}[/tex]
