Rich – AAT (H)
Name: _________________________________
1.4 Day 4/3.1 Quadratic Application Problems
Date: _____________________ Period: _______
Essential Question: How can I do this and how does it apply to my life?
Learning Targets: Students will be able to…
 2.A.9: use quadratic equations to model real life problems.
 2.A.15: solve a quadratic equation using the Quadratic Formula.
For meters: h(t)= -4.9t2+V0t+H0
For feet: h(t)= -16t2+V0t+H0
1) An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. When does the
object strike the ground?
2) An object is launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What
will be the object's hang time?
3) An object is launched from ground level directly upward at 39.2 m/s. For how long is the object at or
above a height of 34.3 meters?
4) After the semester is over, you discover that the math department has changed textbooks (again) so
the bookstore won't buy back your nearly-new book. You and your friend Herman decide to get
creative. You go to the roof of a twelve-story building and look over the edge to the reflecting pool
160 feet below. You drop your book over the edge at the same instant that Herman chucks his book
straight down at 48 feet per second. By how many seconds does his book beat yours into the water?
5) The International Space Agency has finally landed a robotic explorer on an extra-solar planet. Some
probes are extended from the lander's body to conduct various tests. To demonstrate the crushing
weight of gravity on this planet, the lander's camera is aimed at a probe's ground-level ejection port,
and the port launches a baseball directly upwards at 147 feet per second (ft/s), about the top speed of a
professional pitcher. The force due to gravity on this planet is 98 ft/s2. Assuming no winds and that the
probe can scurry out of the way in time, how long will it take for the ball to smack back into the
surface? h(t)= -1/2at2+V0t+H0 where a is acceleration.
6) A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches.
What will be the dimensions of the enlargement?
7) The product of two consecutive negative integers is 1122. What are the numbers?
8) You have to make a square-bottomed, unlidded box with a height of three inches and a volume of
approximately 42 cubic inches. You will be taking a piece of cardboard, cutting three-inch squares from
each corner, scoring between the corners, and folding up the edges. What should be the dimensions of
the cardboard, to the nearest quarter inch?
9) You have a 500-foot roll of fencing and a large field. You want to construct a rectangular playground
area. What are the dimensions of the largest such yard? What is the largest area?
10) Your factory produces lemon-scented widgets. You know that each unit is cheaper, the more you
produce. But you also know that costs will eventually go up if you make too many widgets, due to the
costs of storage of the overstock. The guy in accounting says that your cost for producing x thousands of
units a day can be approximated by the formula C = 0.04x2 – 8.504x + 25302. Find the daily production
level that will minimize your costs.
Practice: Solving Quadratics Mixed Review, pg. 121 #109, 111 and pg. 272 #78c
Rich – AAT (H)
Name: _________________________________
Solving Quadratics Review
Date: ______________________ Period :______
#1 – 3: Solve by graphing (calculator).
1. x 2  5 x  4  0
2. 2 x 2  3x  1
3. x 2  2 x  3
#4 – 6: Solve by factoring (no calculator).
4. 6 x 2  2 x  20
5. x 2  144  0
6. 8 x 3  15 x  14 x 2
#7 – 9: Solve using quadratic formula and round to nearest hundredth (calculator).
7. 4 x 2  3 x  7
8. 3 x 2  4 x  4  5
9.
1 2
x  4x  3  0
3
#10 – 12: Solve using quadratic formula and simplify answer (no calculator).
10. x 2  4 x  5  0
11. 2 x 2  8 x  5
12. 3x 2  4 x  2  0
#13 – 16: Write the equation of the polynomial in standard form with the given roots (no calculator).
13. x  4,  5
15. x  2  3, 2  3
1
3
14. x  , 
2
4
16. x  1  2i
#17 – 18: Use the information provided to solve each problem (calculator).
17. A picture has a square frame that is 2 inches wide. The area of the picture is one-third of the total area
of the picture and frame .What are the dimensions of the picture to the nearest quarter of an inch?
18. An object is launched at an initial velocity of 19.6 meters per second from a 58.8 meter tall platform.
The equation for the object’s height h, in meters, at time t, in seconds, after launch is
h  t   4.9t 2  v0t  h0 , where v0 is the initial velocity and h0 is the initial height. How long is the
object at or above a height of 58.8 meters?
Also complete pg. 121 #109, 111 and pg. 272 #78c