SOLUTION: Jane can kick a soccer ball with a path modelled by h=-(x-19)^2+17, where h is the height of the soccer ball and x is the distance the soccer ball is kicked. Both distances are me

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Jane can kick a soccer ball with a path modelled by h=-(x-19)^2+17, where h is the height of the soccer ball and x is the distance the soccer ball is kicked. Both distances are me      Log On


   

Question 1118687: Jane can kick a soccer ball with a path modelled by h=-(x-19)^2+17, where h is the height of the soccer ball and x is the distance the soccer ball is kicked. Both distances are measured in metres. How far was the ball kicked?
Thank you
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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Both the starting point and the ending point are located at the roots of the quadratic equation


h = 0 = -%28x-19%29%5E2+%2B+17 = 0,     or


%28x-19%29%5E2 = 17,


x%5B1%2C2%5D = +/-sqrt%2817%29+%2B+19.


The difference (= the distance) between the roots  x%5B2%5D = sqrt%2817%29%2B19  and  x%5B1%5D = -sqrt%2817%29%2B19  is  2%2Asqrt%2817%29 = 8.248 meters  (approximately).


Answer.  8.248 meters  (approximately).