Quadratic relation

Question

A rider on mountain one jumps off a ledge. Her path is modelled by the relation h = -0.3d^2 + 1.2d + 1.5, where h is her height above the ground and d is her horizontal distance from the ledge both in meters 

from what height did the rider jump 

find the zeros 

what is her horizontal distance when she hits the ground 

what is her max height above ground 

what is her horizontal distance when she reaches her max height 

Answer 1

When d=0, the rider begins to jump.  This is her initial position.  So to find the height from where she jumped, evaluate h when d=0.

 

To find the zeros, set h=0.   Use the quadratic formula

 

d = (-b ± √(b² - 4ac)) / 2a

 

where:

a = -0.3

b = 1.2

c = 1.5

 

Plug in these values into the formula to solve for d. 

 

To find the distance when she hits the ground, use the zeros that you found.  Choose the positive value of the zero.

 

 

To find her maximum height, we find the vertex.   First, we find the x-coordinate of the vertex.

 

d = -b / (2a)

 

d = - 1.2 / (2 * -0.3)

 

d = 2

 

 

Then evaluate h when d=2.

 

h = -0.3(2)² + 1.2(2) + 1.5

 

h = 2.7

 

 

The vertex is (2, 2.7).

 

 

This means that her maximum height is 2.7 meters at a horizontal distance of 2 meters.