path of an arrow

Question

the path of an arrow released from a bow can be modeled by y=-0.04x^2+4x+5 where X is the horizontal distance in feet and y is the vertical. find & interpret the ordinates of the vertex 

Answer 1

The vertex is the maximum height the arrow reaches.  The vertex has coordinate (h, k).

 

 

We can find the value of h using this formula:

 

h = -b / 2a

 

where:

a = -0.04

b = 4

c = 5

 

h = -4 / (2 * -0.04)

 

h = -4 / -0.08

 

h = 50

 

 

Next, evaluate the k by evaluating y when x=50.

 

k = y(h)

 

k = -0.04(50)² + 4(50) + 5

 

k = 105

 

 

The vertex is (50, 105).  This means that the maximum height is 105 feet at a horizontal distance of 50 feet.