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]}

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