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A sailboat with a sick passenger abroad is following a parabolic path given by the equation y=-x^2+4x+3
 The boat’s captain sent out a distress signal. A speedboat is trying to catch the sailboat to provide medical aid and is on a path given by the linear equation y=x+3  Besides the y-intercept (starting location) where do the paths of the two boats cross? 
 

 Sep 1, 2021
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Just set the quations equal to each other

 

x^2 + 4x + 3 = x + 3

x^2 + 3x = 0

x = 0 or -3       we do not want x = 0  (per the question)

   so x = - 3      us this in either of the equations to find y = 0            (-3,0)

 Sep 1, 2021

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