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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

Guillermo is a professional deep water free diver.\newlineHis altitude (in meters relative to sea level), x x seconds after diving, is modeled by\newlineg(x)=120x(x−100) g(x)=\frac{1}{20} x(x-100) \newlineHow many seconds after diving will Guillermo reach his lowest altitude?\newline□ \square seconds

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Full solution

Q. Guillermo is a professional deep water free diver.\newlineHis altitude (in meters relative to sea level), x x seconds after diving, is modeled by\newlineg(x)=120x(x−100) g(x)=\frac{1}{20} x(x-100) \newlineHow many seconds after diving will Guillermo reach his lowest altitude?\newline□ \square seconds
  1. Find Vertex: To find the lowest altitude, we need to find the vertex of the parabola represented by g(x)=120x(x−100)g(x)=\frac{1}{20}x(x-100).
  2. Vertex Form: The vertex form of a parabola is g(x)=a(x−h)2+kg(x)=a(x-h)^2+k, where (h,k)(h,k) is the vertex. Since the coefficient of x2x^2 is positive, the parabola opens upwards, and the lowest point is the vertex.
  3. Calculate x-coordinate: The xx-coordinate of the vertex is found by using the formula h=−b2ah = -\frac{b}{2a} for a quadratic equation ax2+bx+cax^2 + bx + c. Here, a=120a = \frac{1}{20}, b=−10020b = -\frac{100}{20}, and c=0c = 0.
  4. Calculate h: Calculate h: h=−(−100/20)/(2∗(1/20))=100/40=2.5h=-(-100/20)/(2*(1/20)) = 100/40 = 2.5.

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