h(x)=-0.03(x-14)^2+6. X=horizontal distance traveled in feet. h(x)=height in feet. Write a second function if the kangaroo lands 5 feet farther away

Question

h(x)=-0.03(x-14)^2+6. <----- models a kangaroos jump

It jumps from a higher location and lands 5 feet farther away

Write a second function that represents that and round to the nearest hundredth if necessary 

Answer 1

Hi Kevin,

 

I think what you want to do here, since this equation models the kangaroos height as a function of horizontal distance, is to find the domain of the function and add five to the maximum horizontal, x distance.

 

The kangaroo's maximum height, h(x) is 6 ft at x = 14 ft

You can see that h(x) decreases when x is greater or less than 14

 

The equation is parabolic, so the maximum horizontal distance that can be achieved is ≈ 2*(14 ft) = 28 ft

 

New +5 ft horizontal, x distance:
28 + 5 = 33 ft

h(33) = -0.03(33 - 14)² + 6

Set this equal to zero to find the new maximum height achieved.

0 = -0.03(19)² + 6

0 = -0.03(361) + 6

0 = -10.83 + 6

10.83 = 6

 

So now the kangaroo's maximum height is 10.83 ft instead of 6 ft

replace in the original function

 

h(x) = -0.03(x - 14)² + 10.83

 

Answer 2

The equation models the 

path of the kangaroo's jump,

Parabola.  This means that the

Vertex of the parabola is at the

point (14,6).  If the kangaroo jumps 

out 5 feet further the vertex will move

2.5 feet to the right, making the new

equation:

 

h(x) = -.03 (x - 16.5)² + 6