Question

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)= 1/20x(x-100)

How many seconds after diving will Guillermo reach his lowest altitude?

Answer 1

The lowest altitude will be reached by Guillermo 5 seconds after diving.

Step-by-step explanation:

To find the lowest altitude, we need to determine the vertex of the quadratic function. The vertex of a quadratic function, in the form f(x) = ax^2 + bx + c, is given by the coordinates (-b/2a, f(-b/2a)). In this case, the function is g(x) = (1/20)x(x-100). Comparing it to the standard form, we can see that a = 1/20, b = -100/20 = -5, and c = 0. So, the x-coordinate of the vertex is -(-5)/(2(1/20)) = 5. Substituting this value into the function, we find g(5) = (1/20)(5)(5-100) = -125. Therefore, Guillermo will reach his lowest altitude 5 seconds after diving.