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#?

1 Answer
May 26, 2015

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]}