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

Apr 15, 2015

Range y: $\in$R , y$\le$-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= ${\left(x - 2\right)}^{2}$ +6

x-2= $\sqrt{- y - 6}$

Now for x to be real, -y-6 must be $\ge 0$

-y-6$\ge 0$

-y $\ge 6$
y$\le$-6