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The path of a dolphin underwater is modeled by the equation $P=0.25{x}^{2}-20x+k$ where $P$ is the depth in ft and $x$ is the time in seconds. Determine the lowest depth of the dolphin in terms of $k$.

A

$40k$

B

$40+k$

C

$k+400$

D

$k-400$

E

$k-40$

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