Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level), $$ x $$ seconds after diving, is modeled by $$ g(x)=\frac{1}{20} x(x-100) $$ How many seconds after diving will Guillermo reach his lowest altitude? seconds

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We are given the function modeling Guillermo’s altitude:
  g(x) = (1/20)·x(x – 100).

To find the time when he reaches his lowest altitude, we need to determine the vertex of this quadratic function. First, rewrite the function in standard quadratic form:

g(x) = (1/20)(x² – 100x).

For a quadratic function ax² + bx + c, the vertex (which gives the minimum when a > 0) is at x = –b/(2a). Here, a = 1/20 and b = –100.

Now, calculate the vertex’s x-value:
  x = –(–100) / (2·(1/20)) = 100 / (2/20) = 100 / (0.1) = 50 seconds.

Thus, Guillermo reaches his lowest altitude 50 seconds after diving.
Guillermo reaches his lowest altitude 50 seconds after diving.

Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level), \( x \) seconds after diving, is modeled by \( g(x)=\frac{1}{20} x(x-100) \) How many seconds after diving will Guillermo reach his lowest altitude? seconds

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