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Name_______________________________________________ Date __________ Per _______ Quadratic Applications pt 1 1. The length of a rectangle is x ft and the width is x+6 ft. The area is 91 ft². What are the dimensions of the rectangle? 2. Find the length and width of the rectangle below: 3. The length of a rectangle is 4 meters more than the width. The area is 30 m². Find the length. 4. The length of a rectangular mural is 2 feet more than three times the height. The area is 165 ft². Find the height of the mural. x+3 x15 in²

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5. Find the value of x below. 6. Use the graph to answer the questions. A. If the length of the rectangle is 4, what is the width? B. What is the vertex? What does this point represent? C. What are the x-intercepts? D. What is the domain? Range? 7. A 7 by 10 in mirror was put in a frame and hung on the wall. The mirror and frame cover an area of 130 in². How wide is the frame? 8. Suppose you are building an aquarium with a volume of 2880 in³. the aquarium will be 12 in. high. The base will be a rectangle with the length 4 in. more than twice the width. Find the dimensions of the base. 20 cm² x + 2 x 0 2 4 6 8 10 12 14 16 18 20 Length of the rectangle Area of rectangle 0 5 10 15 20 25 30 35 40 45 50

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Name_______________________________________________ Date __________ Per _______ Quadratic Applications pt 2 Vertical motion formula: 1. The formula gives a ball’s height h in feet at time, t, in seconds. What is the starting height of the ball? _______. What is the velocity? ______. How many seconds pass before the ball lands on the ground? 2. A carnival game involves trying to ring a bell with a ball by hitting a lever that propels the ball into the air. The height of the ball is modeled by the equation. If the bell is 25 ft. above the ground, will you hit tbe ball? (what is the starting height?____) (how fast are you hitting the ball? ____) 3. You launch a model rocket with an upward starting velocity of 160 ft/s. When will the rocket hit the ground? (use the vertical motion formula) What is the starting height? _____ What is the velocity? _____ What is the equation? ________________

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5. Your friend is standing on a balcony which is 38 ft high. You throw a ball up to him with a velocity of 48 ft/s. The ball is 6 ft. high when it leaves your hand. After how many seconds will your friend have a chance to catch the ball? (use the vertical motion formula) Formula: ________________________ 6. The height of a ball is shown in the table: What is the starting height of the ball? What is the maximum height of the ball. ________ Approximately when will the ball reach 30 feet? _________ Will the ball ever reach 50 ft? ____________ Approximately when will the ball hit the ground? ______________ 7. Suppose you throw a ball into the air and the height is given by the formula: What is the height of the ball after 1.5 seconds? __________ Will the ball ever reach 30 ft? 8. A kid throws the ball in the air from a height of 3 ft with a velocity of 10 ft/s. How long will the ball be in the air if no one catches it? (use the vertical motion formula: ___________________) T (Time)H (height) 03.5 0.524.5 137.5 1.542.5 237.5 2.524.5 33.5

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Name _________________________________________ Date_________ Per _______ More Quadratic applications pt1 1. The length of a photograph is 1 cm less than twice the width. The area is 91 cm². Find the length and width. 2. The dimensions of a rectangular flower garden were 8 m by 15 m. Each dimension what increased by the same amount. The garden then had an increased area of 198 m². New length (in terms of x) ________ New width (in terms of x) _________ x = _______ New length _________ New width _________ 3. Hugh Betcha launched a rocket with a speed of 88 ft/s. After how many seconds will the rocket be 40 feet high? (use the vertical motion formula) What is the starting height? _____ Formula ______________ 4. The US populations P in millions where t is the number of years after 1900 is estimated by the equation Estimate the population in the year you graduate from high school. __________________ Estimate the population in 2025. _______________

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Name _________________________________________ Date_________ Per _______ More Quadratic applications pt 2 1. The height of a triangle is x and the base is x+6. If the area is 50 cm² what are the actual dimensions? 2. A football player kicks the ball with an initial upward velocity of 38.4 ft/s from a starting height of 3.5 ft. Use the vertical motion formula to determine how long the ball will be in the air. 3. A diver is standing on a platform 24 ft above the pool. He jumps from the platform with an initial upward velocity of 8 ft/s. Use the vertical motion formula to determine when he will hit the water. 4. You are building a storage box which needs to have a volume of 4368 ft³. The length of the box is 24 in. You want the height to be 1 inch more than its width. Find the height and width of the box.

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