01 May red bird starts his flight from (10,0) and lands at (38,0) after reaches a max. height of
red bird starts his flight from (10,0) and lands at (38,0) after reaches a max. height of 18 yards. So , max. height of red bird’s flight = 18 yards And the total distance covered by red bird is 38 – 10 = 28 yards. It’s graph is shown below : Now , as we have two points of the parabola (10,0) and(38,0) as y value is same , so the axis of symmetry is the vertical line of symmetry between 10 and 38. So , the distance to the middle is (10+38) / 2 = 24. Hence , x = 24 is the axis of symmetry. B. Yellow Bird’s Trajectory Now , we have yellow bird’s flight can be modeled by the quadratic equationy=-x2+14x-24″ role=”presentation” style=”display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: “open sans”; color: rgb(51, 51, 51); position: relative;”>y=-x2+14x-24y=-x2+14x-24 Now , first of all we have to find the starting and landing point of the yellow bird’s flight. So put y = 0 , we get 0 =-x2+14x-24″ role=”presentation” style=”display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: “open sans”; color: rgb(51, 51, 51); position: relative;”>-x2+14x-24-x2+14x-24 Orx2-14x+24″ role=”presentation” style=”display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: “open sans”; color: rgb(51, 51, 51); position: relative;”>x2-14x+24×2-14x+24 = 0.×2-12x-2x+24″ role=”presentation” style=”display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: “open sans”; color: rgb(51, 51, 51); position: relative;”>x2-12x-2x+24×2-12x-2x+24 Therefore , x = 12,2. Hence , yellow bird starts his flight from (2,0) and lands at (12,0). So the total distance covered by yellow bird is 12 – 2 = 10 yards. Now , as we have two points of the parabola (2,0) and(12,0) as y value is same , so the axis of symmetry is the vertical line of symmetry between 2 and 12. So , the distance to the middle is (2+12) / 2 = 7. Hence , x = 7 is the axis of symmetry. Now at the axis of symmetry , yellow bird reaches the max. height So put value of x = 7 in eq. we get y = -49 + 98 – 24 = 25 yards. So , the max. height of the yellow bird’s flight = 25
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