How do you find the domain and range of #y=-2x^2+3#?

1 Answer
Binayaka C.
May 7, 2018

Domain is any real value of #x; x in RR or x in (-oo,oo)#
Range is any real value of #y# less or equal to #3# i.e
# y <=3 or y in (-oo , 3]#

Explanation:

# y= -2 x^2+3 or y= -2 (x-0)^2+3 # Comparing with vertex

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

find here #h=0 , k=3 , a = -2 :.# Vertex is at #(0,3) # Since #a#

is negative the parabola opens downward , therefore vertex is the

maximum point #(0,3)# of the parabola.

Domain is any real value of #x# i.e # x in RR or x in (-oo,oo)#

Range is any real value of #y# less or equal to #3# i.e

# y <=3 or y in (-oo , 3]#

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

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