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Unit 4 Lecture 31 Applications of the Quadratic Formula

Unit 4 Lecture 31 Applications of the Quadratic Formula. Applications of the Quadratic Formula. Objectives. Formulate a quadratic equation from a problem situation Solve a quadratic equation by using the quadratic formula.

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Unit 4 Lecture 31 Applications of the Quadratic Formula

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  1. Unit 4 Lecture 31Applications of the Quadratic Formula Applications of the Quadratic Formula Lecture 31

  2. Objectives • Formulate a quadratic equation from a problem situation • Solve a quadratic equation by using the quadratic formula Lecture 31

  3. You drop a rock from the top of the 1600 feet tall Rears Tower. The height (in feet) of the rock from the ground is given by the equation: h = -16t2 + 1600h is in feet and t is in seconds. How long until the rock hits the ground? Lecture 31

  4. You drop a rock from the top of the 1600 feet tall Rears Tower. The height (in feet) of the rock from the ground is given by the equation: h = -16t2 + 1600h is in feet and t is in seconds. How long until the rock hits the ground? h = -16t2 + 1600 Lecture 31

  5. You drop a rock from the top of the 1600 feet tall Rears Tower. The height (in feet) of the rock from the ground is given by the equation: h = -16t2 + 1600h is in feet and t is in seconds. How long until the rock hits the ground? h = -16t2 + 1600 0 = -16t2 + 1600 Lecture 31

  6. You drop a rock from the top of the 1600 feet tall Rears Tower. The height (in feet) of the rock from the ground is given by the equation: h = -16t2 + 1600h is in feet and t is in seconds. How long until the rock hits the ground? h = -16t2 + 1600 0 = -16t2 + 1600 0 = -16(t2 – 100) Lecture 31

  7. You drop a rock from the top of the 1600 feet tall Rears Tower. The height (in feet) of the rock from the ground is given by the equation: h = -16t2 + 1600h is in feet and t is in seconds. How long until the rock hits the ground? h = -16t2 + 1600 0 = -16t2 + 1600 0 = -16(t2 – 100) 0 = -16(t – 10)(t + 10) Lecture 31

  8. You drop a rock from the top of the 1600 feet tall Rears Tower. The height (in feet) of the rock from the ground is given by the equation: h = -16t2 + 1600h is in feet and t is in seconds. How long until the rock hits the ground? h = -16t2 + 1600 0 = -16t2 + 1600 0 = -16(t2 – 100) 0 = -16(t – 10)(t + 10) (t – 10)=0 or (t + 10)=0 Lecture 31

  9. You drop a rock from the top of the 1600 feet tall Rears Tower. The height (in feet) of the rock from the ground is given by the equation: h = -16t2 + 1600h is in feet and t is in seconds. How long until the rock hits the ground? t = 10 or t =-10 h = -16t2 + 1600 0 = -16t2 + 1600 0 = -16(t2 – 100) 0 = -16(t – 10)(t + 10) (t – 10)=0 or (t + 10)=0 Lecture 31

  10. You drop a rock from the top of the 1600 feet tall Rears Tower. The height (in feet) of the rock from the ground is given by the equation: h = -16t2 + 1600h is in feet and t is in seconds. How long until the rock hits the ground? t = 10 or t =-10 h = -16t2 + 1600 0 = -16t2 + 1600 t = 10 is the only reasonable answer. 0 = -16(t2 – 100) 0 = -16(t – 10)(t + 10) (t – 10)=0 or (t + 10)=0 Lecture 31

  11. The equation for profit is, Profit = Revenue - Cost Revenue:R = 280x -.4x2 Cost: C = 5000 + .6x2 Lecture 31

  12. The equation for profit is, Profit = Revenue - Cost Revenue:R = 280x -.4x2 Cost: C = 5000 + .6x2 P = ( 280x – .4x2) – (5000 + .6x2) Lecture 31

  13. The equation for profit is, Profit = Revenue - Cost Revenue:R = 280x -.4x2 Cost: C = 5000 + .6x2 P = ( 280x – .4x2) – (5000 + .6x2) P = 280x – .4x2– 5000 - .6x2 Lecture 31

  14. The equation for profit is, Profit = Revenue - Cost Revenue:R = 280x -.4x2 Cost: C = 5000 + .6x2 P = ( 280x – .4x2) – (5000 + .6x2) P = 280x – .4x2– 5000 - .6x2 P = -1x2 Lecture 31

  15. The equation for profit is, Profit = Revenue - Cost Revenue:R = 280x -.4x2 Cost: C = 5000 + .6x2 P = ( 280x – .4x2) – (5000 + .6x2) P = 280x – .4x2– 5000 - .6x2 P = -1x2 + 280x Lecture 31

  16. The equation for profit is, Profit = Revenue - Cost Revenue:R = 280x -.4x2 Cost: C = 5000 + .6x2 P = ( 280x – .4x2) – (5000 + .6x2) P = 280x – .4x2– 5000 - .6x2 P = -1x2 + 280x- 5000 Lecture 31

  17. How many items must be made and sold to generate a$439 profit. P = -1x2 + 280x- 5000 Lecture 31

  18. How many items must be made and sold to generate a$439 profit. P = -1x2 + 280x- 5000 439 = -1x2 + 280x- 5000 Lecture 31

  19. How many items must be made and sold to generate a$439 profit. P = -1x2 + 280x- 5000 Subtract 439 from both sides 439 = -1x2 + 280x- 5000 Lecture 31

  20. How many items must be made and sold to generate a$439 profit. P = -1x2 + 280x- 5000 Subtract 439 from both sides 439 = -1x2 + 280x- 5000 0 = -1x2 + 280x- 5439 Lecture 31

  21. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 Lecture 31

  22. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 0 = ax2+ bx + c Lecture 31

  23. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 0 = ax2+ bx + c a = -1 Lecture 31

  24. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 0 = ax2+ bx + c a = -1 b = 280 Lecture 31

  25. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 0 = ax2+ bx + c a = -1 b = 280 c = -5439 Lecture 31

  26. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 0 = ax2+ bx + c a = -1 b = 280 c = -5439 Lecture 31

  27. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 0 = ax2+ bx + c a = -1 b = 280 c = -5439 Lecture 31

  28. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 0 = ax2+ bx + c Lecture 31

  29. Use of the calculator to evaluate a square root. To find the square root of a number, use key in row 6 column 1. is keyed in as 2nd, , 56644, ENTER Lecture 31

  30. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 0 = ax2+ bx + c Lecture 31

  31. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 Lecture 31

  32. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 Lecture 31

  33. Use the Quadratic Formula to solve: 0 = -1x2 + 280x- 5439 Two solutions to make P = $439: x = 21 and x =259 items Lecture 31

  34. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  35. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  36. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  37. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  38. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  39. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  40. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  41. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  42. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  43. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  44. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  45. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  46. Wall Wall Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Make a table and find the formula for the area of the rectangle. W W L Lecture 31

  47. Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Find the dimensions of the rectangle if the area is 65 square inches. Wall Wall A =40X-2X2 W W 65 = -2x2 + 40x L Subtract 65 from both sides Lecture 31

  48. Enclose a rectangle with a 40 inch string and use a wall of the room for one side of the rectangle. Find the dimensions of the rectangle if the area is 65 square inches. Wall Wall A =40X-2X2 W W 65 = -2x2 + 40x L 0 = -2x2 + 40x- 65 Subtract 65 from both sides Lecture 31

  49. Use the Quadratic Formula to solve: 0 = -2x2 + 40x- 65 Lecture 31

  50. Use the Quadratic Formula to solve: 0 = -2x2 + 40x- 65 0 = ax2+ bx + c Lecture 31

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