Question

What is the axis of symmetry and vertex for the graph `y=x^2`?

Answer 1

See the explanation

Explanation:

Consider the standard equation of `y=ax^2+bx+c`

If `a` is positive then the graph is of shape `uu`

If `a` is negative then the graph is of shape `nn`

`color(blue)("In your equation "a=+1" so the graph is of shape "uu)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The `bx` term moves the graph left or right from the y axis.

In your equation `b=0` ( there is no `bx` term)

`color(blue)("In your graph axis of symmetry is the y axis")`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The constant of `c` is the y intercept.

In your equation `c=0` so the y-intercept is the vertex as the axis of symmetry is the y axis

`color(blue)("In your equation the vertex "->(x,y)->(0,0))`