What is the range of the function #y=(x^2) - 6x + 1#?

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Answer 1 · 2017-03-04T01:40:06

Range: [-8, +oo)

#y=x^2-6x+1#

#y# is a parabola with a minimum value where #y'=0#

#y' = 2x-6 =0 -> x=3#

#:. y_min = 3^2 - 6*3 +1 = -8#

#y# has no finite upper limit.

Hence the range of #y# is #[-8, +oo)#

The range of #y# can be deducd by the graph of #y# below.

graph{x^2-6x+1 [-18.02, 18.02, -9.01, 9.02]}