What is the domain and range of # y=-3(x-10)^2+5#?

1 Answer
Nov 10, 2017

Answer:

Domain: #x in RR or (-oo,oo)#
Range: #y<=5 or [-oo,5]#

Explanation:

#y= -3(x-10)^2+5# . This is vertex form of equation of parabola

having vertex at #(10,5) # [ Comparing with vertex form of

equation #f(x) = a(x-h)^2+k ; (h,k)# being vertex we find

here #h=10 , k=5 , a=-3 #] . Since #a# is negative the parabola

opens downward , vertex is the maximum point of #y#.

Domain: Any real number of #x# is possible as input.

So Domain: #x in RR or (-oo,oo)#

Range: Any real number of #y<=5 or [-oo,5]#

graph{-3(x-10)^2+5 [-20, 20, -10, 10]} [Ans]