Answer:
[tex]x=-\frac{2}{3}[/tex]
Step-by-step explanation:
Given its parameters, we know that this quadratic equation represents a parabola with arms pointing down, and with a maximum value at the point of its vertex.
The equation of its axis of symmetry will be a vertical line that goes through that vertex.
Recall that vertical lines have the form: [tex]x=number[/tex].
It is essential then that we find the x coordinate of such vertex to complete the general equation form of this vertical axis.
We use the definition for the x value of the vertex of a parabola of the form:
[tex]y=ax^2+bx+c\\x_{vertex} = -\frac{b}{2a}[/tex]
In our case where [tex]a=-3,\\b=-4,\\c=-8[/tex]
the x-value of the vertex becomes:
[tex]x_{vertex} = -\frac{b}{2a}=-\frac{-4}{2(-3)} = \frac{4}{-6} =-\frac{2}{3}[/tex]
Therefore, the equation for the axis of symmetry of the parabola is:
[tex]x=-\frac{2}{3}[/tex]
