Answer:
the equation of the axis of symmetry is [tex]x=8[/tex]
Step-by-step explanation:
Recall that the equation of the axis of symmetry for a parabola with vertical branches like this one, is an equation of a vertical line that passes through the very vertex of the parabola and divides it into its two symmetric branches. Such vertical line would have therefore an expression of the form: [tex]x=constant[/tex], being that constant the very x-coordinate of the vertex.
So we use for that the fact that the x position of the vertex of a parabola of the general form: [tex]y=ax^2+bx+c[/tex], is given by:
[tex]x_{vertex}=\frac{-b}{2\,a}[/tex]
which in our case becomes:
[tex]x_{vertex}=\frac{-b}{2\,a} \\x_{vertex}=\frac{48}{2\,(3)} \\x_{vertex}=\frac{48}{6} \\x_{vertex}=8[/tex]
Then, the equation of the axis of symmetry for this parabola is:
[tex]x=8[/tex]
