Algebra 2: Quadratic Applications Assessment

General Strategy for Solving Verbal Problems

1. Read the problem carefully. 2. Use diagrams if you think it will make the information clearer. 3. Find the relationship or formula relevant to the problem. 4. Identify the unknown quantity (or quantities), and label them, using one variable. 5. Write an equation involving the unknown quantity, using the relationship or formula from step 3. 6. Solve the equation. 7. Answer the question in a sentence. 8. Check the answer in the original words of the problem.

Your group has been assigned a problem. Your assignment is to solve the problem following the steps above. There is more than one way to solve each problem. Clearly explain how your group solved the problem. You will prepare a poster representing your problem to the class. You will be graded on the following:

Group members ______Period ______

Clear explanation of method used to solve the problem. ____/10 pts

Represent the problem in multiple ways. ____/5 pts

Correct answer. ____/5 pts

Creative and interesting presentation. ____/5 pts

Total ____/25 points A shoe store sells about 200 pairs of a new basketball shoe each month when it charges $60 per pair. For each $1 increase in the price, about 2 fewer pairs per month are sold. How much per pair should the store charge to maximize monthly revenue? What is the maximum revenue?

A rectangle has a perimeter of 23 cm and an area of 33cm2. Find the dimensions

A square piece of cardboard was used to construct a tray by cutting 2-inch squares out of each corner and turning up the flaps. Find the size of the original square if the resulting tray has a volume of 128 cu in.

A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width of the pathway?

An object is launched at 19.6 meters per second (m/s) from a 58.8 meter tall platform. The equation for the object’s height h at the time t seconds after launch is h(t) = -4.9 t2 + 19.6t + 58.8, where h is in meters. When does the object reach it’s maximum height. When does the object strike the ground?

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? The aspect ratio of a TV screen is the ratio of the screen’s width to its height. For most TVs, the aspect ratio is 4:3. What are the width and height of a screen for a 27 inch TV? (Hint: Use Pythagorean theorem and the fact that TV size is such as 27 inches refers to the length of the screen’s diagonal.)

Jackie Joyner-Kersee won the women’s heptathlon during the 1992 Olympics in Barcelona, Spain. Her throw in the shot put, one of the seven events in the heptathlon, can be modeled by y = -.0241x2 + x + 5.5 where x is the shot put’s horizontal distance traveled (in feet) and y is its corresponding height (in feet). How long was Joyner-Kersee’s throw? When did the shot put reach its maximum height?

A farmer has 1200m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing needed along the river. Find the dimensions of the field if the area of the field is 180,000 sq m.