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

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