SOLUTION: Please help me solve this problem A person on the edge of a cliff throws a stone so that it hits the ground near the base of the cliff. The stone's height (in feet above the base)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Please help me solve this problem A person on the edge of a cliff throws a stone so that it hits the ground near the base of the cliff. The stone's height (in feet above the base)      Log On


   

Question 574729: Please help me solve this problem
A person on the edge of a cliff throws a stone so that it hits the ground near the base of the cliff. The stone's height (in feet above the base) h(t) after t seconds is given by the function h(t)= -16t^2+30t+200
a. Find the vertex. What does it mean in this situation?
b. Estimate the height of the cliff
c. Did the person throw the stone upward or downward? Explain.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A person on the edge of a cliff throws a stone so that it hits the ground near the base of the cliff.
The stone's height (in feet above the base) h(t) after t seconds is given by the function h(t)= -16t^2+30t+200
;
a. Find the vertex. What does it mean in this situation?
Use the axis of symmetry formula: x = -b/(2a)
t = %28-30%29%2F%282%2A-16%29
t = %28-30%29%2F%28-32%29
t = .9375 sec
Find the vertex:
h(t)= -16(.9375^2)+30(.9375)+200
h(t) = -14.0625 + 28.125 + 200
h(t) = 214.06 ft
Vertex = .9375, 214.06; the highest point of the stone
:
b. Estimate the height of the cliff
200 ft, h(t) when t=0
:
c. Did the person throw the stone upward or downward? Explain.
Upward, because it's +30t