What is the domain and range of #y = (x – 5)^2 + 10#?

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Answer 1 · 2018-06-13T00:19:48

Domain: #{x|x in RR}#

Range: #{y|y in RR, y>=10}#

You will notice that it is a quadratic equation in "vertex form":

#y=(x+h)^2 +k#

In vertex form the vertex is #(-h,k)#

#y = (x – 5)^2 + 10#

vertex #=(5,10)#

Domain; all quadratic functions have a domain of all real numbers:

Domain: #{x|x in RR}#

Range, since #x# is positive the function opens up and the vertex is a minimum, the #y=10# so the range is:

Range: #{y|y in RR, y>=10}#