A young man is standing on a cliff and shoots an arrow into the air. The height of the arrow can be modeled by the quadratic function:

Question

        

Where  is time in seconds and   is the height in feet after  seconds.

1.  How high is the arrow at 0 seconds?

2. What does this mean in context?

3. How long does it take for the arrow to reach its highest point?

4. How high did it go?

5. Can you find the point on the function that has an ordered pair ( ?, 0)?  What is the value of ?

6. What does this point mean in context?

 

Answer 1

(1)

At t = 0, the height is 110 ft

(2)

h(0) = 110 ft is just the initial height

(3)

It reaches its highest point at the vertex of the height-vs.-time parabola, which is at -B/(2A).

B = 128

A = -16

Plug these two numbers into

t = -B/(2A) and get the time to maximum height in seconds.

(4)

Evaluate h(t) at the value of t that you found in part (3). That will give you h_max.

(5)

Yes. Solve the quadratic equation for h(t) = 0. Use the quadratic formula. You will get a positive and a negative result for t. The correct answer is the positive result.

(6)

It is the point at the bottom of the trajectory.