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)/(20)x(x-100) How many seconds after diving will Guillermo reach his lowest altitude? seconds

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)/(20)x(x-100) How many seconds after diving will Guillermo reach his lowest altitude? seconds

Bytelearn · Accepted Answer

Find Parabola Vertex: To find the lowest altitude, we need to find the vertex of the parabola represented by g(x)=(1/20)x(x-100).Vertex Form Explanation: The vertex form of a parabola is g(x)=a(x-h)^2+k, where (h,k) is the vertex.Calculate x-coordinate of Vertex: The x-coordinate of the vertex, h, is the value of x that makes x(x-100) equal to zero. This is the average of the roots of the equation x(x-100)=0.Find Roots of Equation: The roots of the equation x(x-100)=0 are x=0 and x=100.Calculate Average of Roots: The average of the roots is (0+100)/2 = 50.Final Result: So, the x-coordinate of the vertex is 50, which means Guillermo will reach 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? $\text{seconds}$

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