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Write the formula for the parabola that has x- intercepts (5+ sqrt3 ,0) and (5− sqrt 3 ,0), and y- intercept (0,4)

 Apr 3, 2020
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An equation for a parabola is  y  =  a(x - r)(x -s)  where r and s are x-intercepts.

Placing the two intercepts into this formula, we get:  y  =  a( x - (5 + sqrt(3) )( x - (5 - sqrt(3) )

   --->   y  =  a( x - 5 - sqrt(3) )( x - 5 + sqrt(3) )

           y  =  a(x2 - 10x + 22)

Since the point (0, 4) is on this parabola:

           4  =  a(02 -10·0 + 22)

           4  =  22a

           a  =  2/11

 

y  =  (2/11)(x2 - 10x + 22)

 Apr 3, 2020

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