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Honors Algebra II Worksheet – Applications
1.
Name _____________________________________
Find two numbers whose sum is 36 and whose product is a maximum.
Variables Defined: 1st number: __________ 2nd number: __________
Equation: ___________________________________________________
Equation in vertex form: _________________________________
2.
Vertex: __________________
Answer: ___________________
Find two numbers whose difference is 26 and whose product is a minimum.
Variables Defined: 1st number: __________ 2nd number: __________
Equation: ___________________________________________________
Equation in vertex form: _________________________________
3.
Vertex: __________________
Answer: ___________________
Find the dimensions of a rectangle with perimeter 40cm and maximum area.
Variables Defined: width: __________ length: __________
Equation: ___________________________________________________
Equation in vertex form: _________________________________
4.
Vertex: __________________
Answer: ___________________
George Polo has 120 meters of fence to make a rectangular pen for his rabbits. If a shed is used as one side of the pen, what
would be the length and width for maximum area?
Variables Defined: width: __________ length: __________
Equation: ___________________________________________________
Equation in vertex form: _________________________________
5.
Vertex: __________________
Answer: ___________________
Fred Johnson has 400 yards of fence to make a rectangular corral for his horses. If a river will be used as one side of the corral,
what would be the length and width for maximum area?
Variables Defined: width: __________ length: __________
Equation: _________________________________________________
Equation in vertex form: _________________________________
Vertex: __________________
Answer: ___________________
6. An object is fired upward from the top of a 200 foot tower at a velocity of 80 feet per second. The height of the object above the
ground after t seconds is given by the equation ht    16t 2  80t  200 . What is the maximum height reached by the object? At
what time does the object reach its maximum height?
Equation: ___________________________________________________
Equation in vertex form: _________________________________
Vertex: __________________ Time: __________ Max height: _________
*how would you check this on your calculator? _________________________________
7. A ball is thrown upward into the air at an initial velocity of 64 feet per second. The height of the object above the ground after t
seconds is given by the equation ht    16t 2  64t . What is the maximum height reached by the object? At what time does the
object reach its maximum height?
Equation: ___________________________________________________
Equation in vertex form: _________________________________
Vertex: __________________ Time: __________ Max height: _________
*how would you check this on your calculator? _________________________________
8. For the same ball, ht    16t 2  64t , in how many seconds will the object hit the ground? (what is the height when the ball hits the
ground)
Equation: ___________________________________________________
Answers _______________________
*how would you check this on your calculator? _________________________________