Algebra II
Name______________________________________
Quadratic Word Problems
Period _______ Date _________________________
1. Phoebe was out riding in her spaceship again. This time as she approached the Moon,
she changed her mind and decided not to visit the moon. So she fired her retro rocket
and the ship slowed down, hopefully enough to stop, turned around and went back to
earth. At t = 1, t = 2 and t = 3 her distances are d =560 km, d =362 km and d =208 km
respectively.
a. Find the equation to represent this situation.
b. Find the d-intercept. ______________ What does this tell you about Phoebe’s ride?
c. Find Phoebe’s distance at t = 10 and t = 11 and which direction is she going?
d. Does Phoebe “crash into the moon”, “land and then take off” or “not reach the
moon’s surface?” What tells you this?
e. Graph this function.
2. Matthew was riding in a hot air balloon 256 feet above the ground. He dropped a sand
bag accidentally. The equation h(t )  16t 2  256 is the equation that represents the
path of the sand bag as it falls to the ground.
a. What is the height of the sand bag 2 seconds after Matt dropped it?
b. What is the height of the sand bag 3.5 seconds after Matt dropped it?
c. When did the sand bag hit the ground?
d. Graph this situation using the appropriate domain and range.
e. What is the domain and range for this function?
3. A ball is thrown upward, the equation h(t )  16t 2  32t represents this situation.
a. What is the height of the ball ½ second after it is thrown?
b. When will the ball hit the ground?
c. What is the maximum height of the ball?_______ When did this occur? _______
d. Graph this situation with the appropriate domain and range.
e. What is the domain and range for this function?
4. A sailboat has a sail in the shape of a right triangle. It has an area of 10m 2 . If the height
is 6 less than twice the width, find the width and height of the sail.
5. A rectangular picture has an area of 100cm 2 . The length of the picture is five more than
three times the width. Find the dimensions of the pictures.
6. The volume of the rectangular box is 128m3 . The length is 16m and the height is two
more than the width. Find the dimensions of the box.
7. The sum of a number and its square is 90. What are the two numbers?
8. The positive difference of a number and its square is 240. What are the two numbers?
9. A square is enlarged by two feet on the width side and by three feet on the length side.
The resulting area is 90 ft 2 . Find the dimensions of the original square.