Question

What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function, and x and y intercepts for `y=x^2 - 3`?

Answer 1

Since this is in the form `y=(x+a)^2+b`:

`a=0->`axis of symmetry: `x=0`

`b=-3->` vertex `(0,-3)` is also the y-intercept
Since the coefficient of the square is positive (`=1`) this is a so-called "valley parabola" and the `y`-value of the vertex is also the minimum.
There is no maximum, so the range: `-3<=y< oo`

`x` may have any value, so domain: `-oo < x<+oo`

The x-intercepts (where y=0) are `(-sqrt3,0)and(+sqrt3,0)`
graph{x^2-3 [-10, 10, -5, 5]}