Dolphins jump out of the water, or breach, for a number of reasons, including communication, display, and feeding. A scientist is tracking the movement of a dolphin as it breaches. The dolphin's distance above or below the surface of the water, in feet, after t seconds can be modeled by the expression –16(t–1.5)2+19.Complete the sentence.The dolphin jumped out of the water and reached a maximum height of feet above the water's surface.
Question
Dolphins jump out of the water, or breach, for a number of reasons, including communication, display, and feeding. A scientist is tracking the movement of a dolphin as it breaches. The dolphin's distance above or below the surface of the water, in feet, after t seconds can be modeled by the expression –16(t–1.5)2+19.Complete the sentence.The dolphin jumped out of the water and reached a maximum height of feet above the water's surface.
Solution
The expression given is a quadratic function, which models the motion of the dolphin. The maximum height of the dolphin above the water's surface is given by the vertex of the parabola represented by this function.
The general form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the function is y = -16(t - 1.5)^2 + 19.
Comparing this with the general form, we can see that the vertex of the parabola, and thus the maximum height of the dolphin, is 19 feet.
So, the completed sentence is: "The dolphin jumped out of the water and reached a maximum height of 19 feet above the water's surface."
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