Question

Find the equation of the axis of symmetry of the following parabola algebraically.

Answer 1

Answer:

the equation of the axis of symmetry is $x=8$

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: $x=constant$, 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: $y=ax^2+bx+c$, is given by:

$x_{vertex}=\frac{-b}{2\,a}$

which in our case becomes:

$x_{vertex}=\frac{-b}{2\,a} \\x_{vertex}=\frac{48}{2\,(3)} \\x_{vertex}=\frac{48}{6} \\x_{vertex}=8$

Then, the equation of the axis of symmetry for this parabola is:

$x=8$