juliamixon juliamixon
  • 08-11-2016
  • Mathematics
contestada

What is the maximum vertical distance between the line y = x + 56 and the parabola y = x2 for −7 ≤ x ≤ 8?

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scme1702
scme1702 scme1702
  • 12-11-2016
-7 and 8 are the solutions to the given equation system.
Therefore, the maximum distance between the y values of the two equations must lie exactly between their points of intersection. That is on x value:
x = (-7 + 8)/2 = 0.5
The maximum distance is:
y = 0.5 + 56 = 56.5
y = 0.5² = 0.25
56.5 - 0.25 = 56.25 units
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