How do you find the domain and range of #h(x) = (x - 2)^2 + 2#?

1 Answer
Jul 26, 2018

Answer:

#x inRR,y in[2,oo)#

Explanation:

#"This is a polynomial of degree 2 and is well defined for all"#
#"real values of "x#

#"domain is "x inRR#

#(-oo,+oo)larr color(blue)"in interval notation"#

#"To obtain the range we require the vertex and whether"#
#"it is a max/min turning point"#

#"The equation of a parabola in "color(blue)"vertex form"# is.

#•color(white)(x)y=a(x-h)^2+k#

#"where "(h,k)" are the coordinates of the vertex and a is"#
#"a multiplier"#

#y=(x-2)^2+2" is in this form"#

#color(magenta)"vertex "=(2,2)#

#"Since "a>0" then minimum turning point "uuu#

#"range is "y in[2,+oo)#
graph{(x-2)^2+2 [-10, 10, -5, 5]}