Find the vertex of the parabola.
$h (x) = - x^{2} + 4 x - 4$

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Answer

$Final Answer: The vertex of the parabola is at the point (2, 0)$

Steps

Step 1 ：The given function is $h (x) = - x^{2} + 4 x - 4$ .

Step 2 ：The vertex of a parabola given in the form $f (x) = a x^{2} + b x + c$ is at the point $(- b / 2 a, f (- b / 2 a))$ .

Step 3 ：In this case, $a = - 1$ , $b = 4$ , and $c = - 4$ .

Step 4 ：So, the x-coordinate of the vertex is $- b / 2 a = - 4 / (- 2) = 2$ .

Step 5 ：We can substitute $x = 2$ into the equation to find the y-coordinate of the vertex.

Step 6 ：Substituting $x = 2$ into the equation gives $y = 0$ .

Step 7 ： $Final Answer: The vertex of the parabola is at the point (2, 0)$