The quadratic function g models the depth, in meters, below the surface of the water of a seal t minutes

Question

The quadratic function g models the depth, in meters, below the surface of the water of a seal t minutes after the seal entered the water during a dive. The function estimates that the seal reached its maximum depth of 302.4 meters 6 minutes after it entered the water and then reached the surface of the water 12 minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal 10 minutes after it entered the water?

Accepted Answer

The correct answer is 168 . The quadratic function g gives the estimated depth of the seal, g t , in meters, t minutes after the seal enters the water. It's given that function g estimates that the seal reached its maximum depth of 302.4 meters 6 minutes after it entered the water. Therefore, function g can be expressed in vertex form as g t = a t - 6 2 + 302.4 , where a is a constant. Since it's also given that the seal reached the surface of the water after 12 minutes, g 12 = 0 . Substituting 12 for t and 0 for g t in g t = a t - 6 2 + 302.4 yields 0 = a 12 - 6 2 + 302.4 , or 36 a = - 302.4 . Dividing both sides of this equation by 36 gives a = - 8.4 . Substituting - 8.4 for a in g t = a t - 6 2 + 302.4 gives g t = - 8.4 t - 6 2 + 302.4 . Substituting 10 for t in g t gives g 10 = - 8.4 10 - 6 2 + 302.4 , which is equivalent to g 10 = - 8.4 4 2 + 302.4 , or g 10 = 168 . Therefore, the estimated depth, to the nearest meter, of the seal 10 minutes after it entered the water was 168 meters.

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