Question

Flying fish use their pectoral fins like airplane wings to glide through the air. Suppose a flying fish reaches a maximum height of 5 ft after flying a horizontal distance of 33 ft. Write a quadratic function y=a(x-h)^2+k that models the flight path assuming the fish leaves the water at (0,0). Describe how the changing value of a,h, or k affects the flight path

Answer 1

The flight is in the shape of a parabola with a vertex 5 feet above the water and  1/2 * 33 = 16.5 feet horizontally from the point of leaving the water

y = a(x - h)^2 + k

where  (h,k)  is the vertex of the  parabola and here it is (5 , 16.5), so we have the function:-

y = a(x - 16.5)^2 + 5

when x = 0 y = 0  so

0 = a(-16.5)^2 + 5

which gives a = -0.018365

So our function for the flight path is

y = -0.018365(x - 16.5)^2 + 5     Answer

Answer 2

Answer:

Equation: $y= -0.00459*(x-33)^{2} + 5$

Step-by-step explanation:

Using the value as height in axis y, and horizontal distance in axis x

$y=a*(x-h)^{2}+k\\ h=33\\k=5\\y=a*(x-33)^{2}+5$

X=0, Y=0

$y=a*(x-33)^{2}+5\\ 0=a*(0-33)^{2}+5\\a=-\frac{5}{33^{2} } =-0.00459$

In the figure can see the motion of the fish while flying like airplane