Parabola of the Week
Choose one of the four problems.
· Restate your problem.
· Present neat and organized answers to each of the questions asked.
· SHOW all work, including calculations involving the quadratic formula.
· Round answers to the nearest hundredth when necessary.
· Illustrate your paper (if not illustrating by hand, cite any sources you use for your graphics).
· Use 8.5 by 11 inch paper (maximum size).
· You may show calculations and your graph in pencil, but the rest of your final copy should be in ink (by pen or by printer).
· Due Friday, March 25
Option 1: Choose a problem involving distance in FEET
The height of an object (in feet) after t seconds is given by h = -16t2 + rt + d where
h = height in feet, r = initial upward velocity in feet per second, t = time traveled in seconds, and d = initial starting point (in feet).
Basketball Problem
Stephen Curry throws a basketball straight up in the air from a height of 5 feet with an initial upward velocity of 30 feet per second.
1. Write a function relating the ball’s height above the ground as a function of time.
2. Analyze your function: Identify the axis of symmetry, the vertex, and the zeros for your function. (Incorporate this vocabulary into your answers below. )
3. Make a T-table with 5 ordered pairs.
4. Graph the function.
5. How high above the ground does the ball get?
6. After how many seconds does the ball reach this maximum height?
7. After how many seconds does the ball land on the ground?
Snoopy Problem
Snoopy is in his Sopwith Camel, 4,000 feet above the ground. He fires a missile at the Red Baron with an initial upward velocity of 320 feet per second. The Red Baron is 4,700 feet above the ground.
1. Write a function showing height as a function of time.
2. Analyze your function: Identify the axis of symmetry, the vertex, and the zeros for your function. (Incorporate this vocabulary into your answers below. )
3. Make a T-table with 5 ordered pairs.
4. Graph the function.
5. When, on the way up, would the missile hit the Red Baron?
6. If the missile misses the Red Baron on the way up, what is the maximum height it will reach?
7. If the missile misses the Red Baron on the way up, when (t = ?) might the missile hit the Red Baron on the way down?
8. What if the missile misses the Red Baron all together? When will it land?
Apple Toss Problem
Mitch tossed an apple to Kathy, who was on a balcony 40 feet above him, with an initial speed of 56 feet/second. Kathy missed the apple on its way up, but caught it on its way down.
1. Write a function showing the height of the apple in relation to time.
2. Analyze your function: Identify the axis of symmetry, the vertex, and the zeros for your function. (Incorporate this vocabulary into your answers below. )
3. Make a T-table with 5 ordered pairs.
4. Graph the function.
5. What was the apple’s maximum height?
6. When did the apple reach its maximum height?
7. How long was the apple in the air? (Kathy caught the apple at a height of 40 feet)
8. If Kathy missed the apple, after how many seconds did it land?
9. Identify the axis of symmetry, the vertex, and the zeros for your function. (Incorporate this vocabulary into your answers for 2, 3, and 4 above.)
10. Make a T-table with 5 ordered pairs.
11. Graph the function.
Option #2: Choose a problem involving distance in meters
The height of an object (in meters) after t seconds is given by h = -4.9t2 + rt + d where
h = height in meters, r = initial upward velocity in meters per second, t = time traveled in seconds, and d = initial starting point (in meters).
Diving Problem
Abby Johnston jumps off the 10 meter diving platform with an initial velocity of 3.8 meters per second.
1. Write a function showing Abby’s height above the water as a function of time.
2. Analyze your function: Identify the axis of symmetry, the vertex, and the zeros for your function. (Incorporate this vocabulary into your answers below. )
3. Make a T-table with 5 ordered pairs.
4. Graph the function.
5. How high above the water does Abby get?
6. When does she reach this maximum height?
7. When does Abby hit the water?
Don’t forget to round answers to the nearest hundredth!