Question

How do you find the axis of symmetry and vertex point of the function: #y=3x^2+3 #?

Answer 1

Axis of symmetry: `x=0`
Vertex: `(0,3)`

Explanation:

Note that any parabolic equation of the general form:
`color(white)("XXX")y=ax^2+bx+c`
has a vertical axis of symmetry.

`y=3x^2+3color(white)("XXX")iffcolor(white)("XXX")y=3x^2+0x+3`
is in this general form.

Further, it can be re-written as
`color(white)("XXX")y=3(x-color(red)(0))^2+color(blue)(3)`
which is the vertex form with a vertex at `(color(red)(0),color(blue)(3))`

Its (vertical) axis of symmetry (i.e. `x=c` for some constant `c`) must pass through the vertex
therefore, the axis of symetry is
`color(white)("XXX")x=color(red)(0)`