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find the quadratic function that pass through (-3,0) (1,-6) (5,0)

 May 31, 2021
 #1
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x = -3    and   x  = 5        are roots.....and  ( 1, -6)   is  on the  graph.....so.......we  have  this

 

-6  =  a(1+3)  (1 - 5)      simplify

 

-6  = a   (4)  ( - 4)

 

-6  = (-16)a

 

a  = -6/-16 = 3/8

 

So......the  function  is

 

f(x)  =   (3/8)  ( x + 3) ( x - 5)

 

f(x)  = (3/8) ( x^2  -2x   - 15)

 

f(x)  = (3/8)x^2 - (3/4)x  - 45/8

 

See  the  graph here  :   https://www.desmos.com/calculator/aqoish07nx

 

 

cool cool cool

 May 31, 2021

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