What is the range of the function #-x^2 + 4x -10#?

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Answer 1 · 2017-04-28T07:06:14

#(-oo, -6]#

#f(x) = -x^2+4x-10#

Since the coefficient of #x^2# is negative, the quadratic function, #fx)# will have a maximum value.

#f'(x) = -2x+4#

#:. f(x)# will have a maximum value where: #-2x+4=0#

#2x=4 -> x=2#

#:. f_"max" = f(2) = -4+8-10 = -6#

#f(x)# has no lower bound.

Hence the range of #f(x)# is #(-oo, -6]#

This can be seen from the graph of #f(x) below.

graph{-x^2+4x-10 [-37.43, 44.77, -32.54, 8.58]}