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A parabolic arch has a height of 25 feet and a span of 40 feet. How high is the arch 8 feet from each side of the center?

 Apr 7, 2020
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Let  the point  on the ground directly  below the  center of the top of the arch  = (0,0)

 

Then  the points  ( 0, 25)  ( 20, 0)  and (-20, 0)  are  on the graph of the parabola

 

We  have  this

 

25  = a ( 0 - 20)  ( 0 + 20)

 

25  = a (-400)

 

a = 25 / -400  =  -1/16

 

So  we  have  the  form

 

y = (-1/16) ( x- 20) ( x + 12)

 

8  feet from the center  is the  point  (8,0)

 

So...the  height at that point can be found as

 

(-1/16) ( 8 + 20) (8 - 20)  =

 

(-1/16) (28) (-12)  =

 

(12/16) (28) = 

 

(3/4) (28)  =

 

3 (28/4)  = 

 

3 * 7  =  

 

21 ft

 

 

cool cool cool

 Apr 7, 2020

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