Question

In Exercises 65 and 66 use the following information. A bottlenose dolphin jumps out of the water. The path the dolphin travels can be modeled by \(h=-0.2 d^{2}+2 d,\) where \(h\) represents the height of the dolphin and \(d\) represents horizontal distance. What is the maximum height the dolphin reaches?

Short answer

Therefore, the maximum height that the dolphin reaches is 5 units.

Step-by-step solution

Determine the Values of a and b in the Given Function

From the quadratic function \( h=-0.2d^{2}+2d \), we can see that \( a = -0.2 \) and \( b = 2 \). We don't require the value of \( c \) as it won't be used in our calculation to find the maximum height.

Calculate the Value of d at the Vertex of the Parabola

Substitute the values of \( a \) and \( b \) into the formula \( d = -b/{2a} \). \nSo, \( d = -2/{-0.4} = 5 \)

Substitute the Value of d into the Function

The maximum height is obtained by substituting \( d = 5 \) into the quadratic function \( h = -0.2*(5)^{2}+2*5 \), which gives \( h = 5 \).