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Do NOW

Do NOW. Solve this equation using Complete the Square: 1) x 2 – 9 x + 20 = 0 Solve these equation using Quadratic Formula 2) –2 x 2 + 3 x = 9. Page 95. Quiz. Change #2 to x 2 + 4 x – 2 = 0. Quadratic Formula Applications. Section 2.3. How to Solve.

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  1. Do NOW Solve this equation using Complete the Square: 1) x2 – 9x + 20 = 0 Solve these equation using Quadratic Formula 2) –2x2 + 3x = 9 2.3: Quadratic Applications

  2. Page 95 2.3: Quadratic Applications

  3. Quiz Change #2 to x2 + 4x – 2 = 0 2.3: Quadratic Applications

  4. Quadratic Formula Applications Section 2.3 2.3: Quadratic Applications

  5. How to Solve • Read the problem 3 times. Once to read it, a second time to note all critical information, and lastly to determine the equation needed and what is being asked for. • Determine the variables • Draw a picture if applicable. • Translate from English to Math. • Solve for at least one variable. • Find any remaining information. • Interpret your answer. 2.3: Quadratic Applications

  6. Example 1 The sum of two numbers is 15 and the difference of the squares is 5. What are the numbers? 2.3: Quadratic Applications

  7. Example 2 The sum of the squares of two consecutive integers is 4513. What are the positive numbers? 2.3: Quadratic Applications

  8. Your Turn The product of 2 consecutive positive odd integers is 195. Find the numbers. 2.3: Quadratic Applications

  9. Example 3 A rectangle is twice as wide as it is high. If it has an area of 24.5 in2, what are its dimensions? 2.3: Quadratic Applications

  10. Example 3 A rectangle is twice as wide as it is high. If it has an area of 24.5 in2, what are its dimensions? 2.3: Quadratic Applications

  11. Your Turn A rectangle has a perimeter of 45 cm. and an area of 112.5 cm2. What are its dimensions? 2.3: Quadratic Applications

  12. Example 4 A rectangle is 7 cm long and 4 cm wide. When each dimension is increased by x cm, the area is tripled. Find x. Tripled Area Original Area 5-6: Quadratic Formula Applications

  13. Example 4 A rectangle is 7 cm long and 4 cm wide. When each dimension is increased by x cm, the area is tripled. Find x. Tripled Area 5-6: Quadratic Formula Applications

  14. Example 5 A walkway of uniform width has area 72 meters2 (perimeter) and surrounds a swimming pool that is 8 meters wide and 10 meters long. Find the width of the walkway. 5-6: Quadratic Formula Applications

  15. Example 5 A walkway of uniform width has area 72 meters2 (perimeter) and surrounds a swimming pool that is 8 meters wide and 10 meters long. Find the width of the walkway. 5-6: Quadratic Formula Applications

  16. Example 6 The average of 2 real numbers is 41.125 and their product is 1,683. What are the two numbers? 2.3: Quadratic Applications

  17. Example 6 The average of 2 real numbers is 41.125 and their product is 1,683. What are the two numbers? 2.3: Quadratic Applications

  18. Example 6 The average of 2 real numbers is 41.125 and their product is 1,683. What are the two numbers? 2.3: Quadratic Applications

  19. Example 6 The average of 2 real numbers is 41.125 and their product is 1,683. What are the two numbers? 2.3: Quadratic Applications

  20. Your Turn A landscaper wants to put a cement walk of uniform width around a rectangular garden that measures 24 by 40 feet. She has enough cement to cover 660 feet2. How wide should the walk be in order to use the cement? 2.3: Quadratic Applications

  21. Example 7 A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown? 2.3: Quadratic Applications

  22. Example 7 A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown? 2.3: Quadratic Applications

  23. Example 7 A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown? 2.3: Quadratic Applications

  24. Example 7 A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown? 2.3: Quadratic Applications

  25. Your Turn To get to work, Sam jogs 3 miles to the train station, then rides the remaining 5 miles. If the train goes 40 miles per hour faster than Sam’s constant rate of jogging and the entire trip takes 30 minutes (use ½ hour), how fast does Sam jog per hour? 2.3: Quadratic Applications

  26. Assignment Worksheet 2.3: Quadratic Applications

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