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 Quadratic Functions 20-1; completing the square

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Annette takes a jump on her snowmobile and lands on a level snowfield several meters from her takeoff point. Her path through the air could be described using the function y= -0.25x^2 + 2.5x where x and y are measured in meters.

 

Determine the distance horizontally from the takeoff point to where Annette landed.

 Jan 16, 2024
edited by DanStar  Jan 16, 2024

1+0 Answers

 #1
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Write as

 

-(1/4)x^2 + (5/2)x  =  0

 

Find the roots

 

 

Factor as

 

-x [ (1/4)x - (5/2)  ]  = 0

 

Set the factors  to  0 and  solve  for  x

 

-x  =  0            (1/4)x - (5/2)   =0

x  = 0              (1/4)x = (5/2)

                              x = (5/2)(4/1)  = 10

 

The roots are

 

x = 0   and  x  = 10

 

The horizontal dstance =  10 -  0    =    10 (meters)

 

 

cool cool cool

 Jan 16, 2024

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