How do you find the domain and range of #y=x^2 +2x -5#?

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Answer 1 · 2017-07-09T03:09:04

Domain: #(-oo, +oo)#
Range: #[-6, +oo)#

#y=x^2+2x-5#

#y# is defined #forall x in RR#
Hence the domain of #y# is #(-oo, +oo)#

#y# is a quadratic function of the form #ax^2+bx+c#

The graph of #y# is a parabola with vertex where #x=(-b)/(2a)#

Since the coefficient of #x^2>0# the vertex will be the absolute minimum of #y#

At the vertex #x= (-2)/(2xx1) = -1#

#:. y_min = y(-1) = 1-2-5 = -6#

Since #y# has no upper bound the range of #y# is [-6, +oo)

As can be seen on the graph of #y# below.

graph{x^2+2x-5 [-16.02, 16.02, -8.01, 8.01]}