What is the domain and range of -2(x-4)^2+8 ?

1 Answer
Jim G.
Jun 22, 2018

#x inRR,y in(-oo,8]#

Explanation:

#-2(x-4)^2+8" is a parabola and is defined for all real "#
#"values of "x#

#"domain is "x inRR#

#-oo,oo)larrcolor(blue)"in interval notation"#

#"for the range we require the vertex and whether "#
#"maximum/minimum"#

#"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"#

#-2(x-4)^2+8" is in this form"#

#"with vertex "=(4,8)#

#"since "a <0" then maximum turning point " nnn#

#"range is "y in(-oo,8]#
graph{-2(x-4)^2+8 [-20, 20, -10, 10]}

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