OG详解-OG8 数学2 Q27

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 36a=-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.