How would I algebraically find the range of #-x^2 + 4x -10#?

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Answer 1 · 2015-04-15T18:38:15

Range y: #in#R , y#<=#-6

Write y = - #x^2# +4x -10 or,
-y = #x^2# -4x+10. Now solve for a as follows:

-y= #x^2# -4x +4-4+10

-y= #(x-2)^2# +6

x-2= #sqrt(-y-6)#

Now for x to be real, -y-6 must be #>=0#

-y-6#>=0#

-y #>=6#
y#<=#-6