f(x)=x^2-3It's for Functions. How is this done?

(Sice this to be a college level subject from your
address, I would like to cover the answer analysing the perspective of the function and
tracing it by the properties of the function).

f(x) = x^2-3
as a function represents parabola. It is a function of  second
degree.

Also we can write y =
x^2-3.

Symmetry: The curve is symmetrixcal about y axis as
for x and -x  the function gives the same positive y
value.

Vertex : The vertex of the cuve is  (0,
-3)

The cuve is open upwards and goes for positive ifinite
values on both left and right as x becomes large and
large.

The curve, obviously ,has a value of -3 lowest when
x=0. And that y= -3 ids the intercept value of the cuve on the Y
axis.

The curve as crosses the x axis at equal distances of
sqrt3 on the right and -sqrt3 on the left.

The curve y=
x^2-3 Or x^2 = y+3or parabola has Could be compares to
a

X^2 = 4aX a standard parabola. So we can write x^2 =
4(1/4) (y+y). So a= 1/4 is the focal length and (0, -3+1/4) or (0, -11/4 ) are the co
ordinate positions of the focus. And the equation of the directrix is  y = -3-1/4 . Or y
= -13/4 a parallel line to X axis .