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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 ht 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 ht 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, ht 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? _________________________________