Length of a Side (m)
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1 Quadratics Day 1 The graph shows length and area data for rectangles with a fixed perimeter. Area (m ) Length of a Side (m) 1. Describe the shape of the graph and any special features you observe.. What is the greatest area possible for a rectangle with this perimeter? What are the dimensions of this rectangle? 3. What is the fixed perimeter for the rectangle represented by the graph? Explain how you found the perimeter. 4. What is the area of the rectangle with a side of length 1 meters? What is the area of the rectangle with a side of length 8 meters? Explain how these two rectangles are related. 5. What are the x-intercepts of the function? 6. What is the vertex of the function and is it a maximum or minimum point?,
2 Quadratics Day 1 The table shows length and area data for rectangles with a fixed perimeter. Complete the data for the width. 7. How do the shape and special features you observed in the graph from # 1 appear in the table? 8. What is the fixed perimeter for the rectangles represented in the table? Explain how you found the perimeter. 9. What is the greatest area possible for a rectangle with this perimeter? Length of a side (m) Width of a side (m) Area (m ) What are the dimensions of this rectangle? Graph a parabola with the given vertex and x-intercepts. Answer the other two parts. 10. Vertex: (4, 3) x-intercepts (or roots): (, 0) and (6, 0) Maximum or Minimum point? Equation of the Line of Symmetry
3 Quadratics Day 1 Identify the parts of each quadratic function. Draw the line of symmetry for each function. 11. Vertex O Maximum or Minimum point? Equation of the Line of Symmetry x-intercepts (or roots) 1. Vertex Maximum or Minimum point? Equation of the Line of Symmetry x-intercepts (or roots) 13. Vertex Maximum or Minimum point? Equation of the Line of Symmetry x-intercepts (or roots)
4 Quadratics Day Complete the following. Engineer Erik launched a model rocket from the top of a building that is 80 feet tall. The rocket has an initial upward speed of 160 feet per second. The path of the rocket can be modeled by the following equation: h -16t 160t Complete the table.. Graph the path of the rocket. Time (in sec.) Process Height (in ft.) 3. What is a reasonable domain for this graph? 4. What is a reasonable range for this graph? 5. What is the height of the rocket at 3 seconds? 6. How long will it take the rocket to reach 336 feet in height? 7. At how many seconds will it be 444 feet in height? 8. How long will it take to reach maximum height? 9. What is the maximum height? 10. Will the rocket go higher than 500 feet?
5 Quadratics Day Judging by his past performance on mathematics exams, Studious Stanley can estimate the grade he will receive on a mathematics exam using the function, G ( t ) t 8t 78, where t represents the number of hours that he spends studying. 11. What is his grade if he spends 3 hours studying? 1. How many hours did he study, if his grade is 7? 13. What is his grade if he only studies hours? 14. Is there another time where he will have the same grade? 15. How many hours should he study to reach his maximum grade? 16. What is his maximum grade? 17. What is a reasonable range for this situation? Athletic Adam threw a ball straight up with an upward speed of 40 feet per second. His hand was 8 feet above the ground when he released the ball. Write a function that models the path of the ball. (Use the formula, h 16t 40t 8.) 18. How long was the ball in the air? 19. What was the maximum height of the ball? 0. How long did it take to reach maximum height? 1. After it reached maximum height, how long did it take to drop to Earth?. What is a reasonable domain for this situation?
6 Quadratics Day 3 Assignment Date Per. Batter Brandon hit a baseball upward with an initial speed of 10 feet per second. How much later did Ollie Outfielder catch the ball? (Use the formula, h 16t vt.) 1. If v = initial velocity (initial speed), what is the initial velocity?. What is the function? 3. What was the maximum height of the ball? 4. How long did it take to reach maximum height? 5. How much later did Ollie catch the ball? 6. What is a reasonable domain for this situation? Bart tossed an apple to Starr, who was on a balcony 40 feet above him, with an initial velocity of 56 feet per second. Starr missed the apple on the way up, but caught it on the way down. How long was it in the air? (Use the formula, h 16t vt.) 7. If v = initial velocity (initial speed), what is the initial velocity? 8. What is the function? 9. What was the maximum height of the apple? 10. How long did it take to reach maximum height? 11. How long was the apple in the air? 1. What is a reasonable range for this situation? A signal flare is fired upward with an initial speed of 45 meters per second. A stationary balloonist at a height of 1960 meters sees the flare on its way up. How long after this will the flare pass the balloonist again on the way down? (Use, h 4.9t vt s.) 13. What is the initial velocity? 14. What is the starting height? 15. What is the function? 16. How long was the flare at least 940 meters above the ground? 17. What is the maximum height of the flare? 18. How long was the flare in the air?
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