Answer
Evaluate $k(x) = -x^2 - 2x +3$:
$k(0) = 3$
$k(2) = -5$
$k(-2) = 3$
$k(\sqrt 2) = 1 - 2\sqrt2 = -1.828$
$k(a+2) = -a^2-6a-3$
$k(-x) = -x^2+2x+3$
$k(x^2) = -x^4-2x^2+3$
Work Step by Step
For x = 0
$k(0) = -(0)^2 - 2(0) +3$... square 0
$=-(0) - 2(0) +3$...multiply 0 by -1
$=0-2(0)+3$...multiply 0 by 2
$=0-0+3 = 3$
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For x = 2
$k(2) = -(2)^2 - 2(2) +3$... square 2
$=-(4) - 2(2) +3$...multiply 4 by -1
$=-4-2(2)+3$...multiply 2 by 2
$=-4-4+3 = -5$
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For x = -2
$k(-2) = -(-2)^2 - 2(-2) +3$... square -2
$=-(4) - 2(-2) +3$...multiply 4 by -1
$=-4-2(-2)+3$...multiply -2 by 2
$=-4-(-4)+3 = 3$
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For x = $\sqrt 2$
$k(\sqrt 2) = -(\sqrt 2)^2 - 2(\sqrt 2) +3$... square $\sqrt 2$
$=-(2) - 2(\sqrt 2) +3$...multiply 2 by -1
$=-2-2\sqrt 2+3$...simplify
$=1 - 2\sqrt2 = -1.828$
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For x = a + 2
$k(a+2) = -(a+2)^2 - 2(a+2) +3$... square $a + 2$
$=-(a^2+4a+4) - 2(a+2) +3$...multiply quadratic by -1
$=-a^2-4a-4-2(a+2)+3$...multiply $a+2$ by -2
$=-a^2-4a-4-2a-4+3$...simplify
$=-a^2-6a-5$
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For x = -x
$k(-x) = -(-x)^2 - 2(-x) +3$... square -x
$=-(x^2) - 2(-x) +3$...multiply $x^2$ by -1
$=-x^2-2(-x)+3$...multiply -x by -2
$=-x^2+2x+3$
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For x = $x^2$
$k(x^2) = -(x^2)^2 - 2(x^2) +3$... square $x^2$
$=-(x^4) - 2(x^2) +3$...multiply $x^4$ by -1
$=-x^4-2(x^2)+3$...multiply $x^2$ by -2
$=-x^4-2x^2+3$
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