How do you find the domain and range of h(x) = (x - 2)^2 + 2?
1 Answer
Jul 26, 2018
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]}
