# Can someone tell me the range and domain of these functions? Thanks? Relevance
• The domain is all real numbers for both functions.

(-infinity, + infinity)

There are no restrictions on the domain.

Range:

Both functions are parabolas.

Vertex format is:

y = a(x-h)^2  + k

has vertex (h,k)

if a is positive, the parabola turns upward

if a is postive,  the range is y>=k

if a is negative,  the parabola turns downward

if a is negative, the range is is y<= k

1st parabola is already in vertex format

y = 2(x+2)^2  + 3

vertex ( -2, 3)

and "a" = + 2 , the parabola goes upward from the vertex (-2,3)

so range is   y >=  3

2nd parabola

convert to vertex format

y=-2x^2 -8x +3   = -2(x^2 + 4x)   + 3

but (x+2)^2 = x^2 + 4x  + 4

so

x^2 + 4x  = (x+2)^2 - 4

now, substitute  " (x+2)^2 -4"  for x^2 +4x

y=   -2( (x+2)^2 -4)   + 3

y = -2(x+2)^2   + 8 + 3

y = -2(x+2)^2   + 11

so vertex  (-2, 11)

and "a" is negative , so the parabola goes

downward  from the vertex  (-2,11)

so range is  y<= 11

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