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Find a+b+c if the graph of the equation y=ax^2+bx+c is a parabola with vertex (5,3), vertical axis of symmetry, and contains the point (2,0).

 Jul 12, 2019
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Find a+b+c if the graph of the equation y=ax^2+bx+c is a parabola with vertex (5,3), vertical axis of symmetry, and contains the point (2,0).

 

(2.0)  means that x  =  2  is a root

 

The x  value of the other root is  given by

 

[ 2 + x ]

_______   =        5               multiply through by 2

     2

 

2 + x  =  10             subtract  2 from both sides

 

x  = 8

 

So.....the other root is   (8, 0)

 

So  we have that

 

y  =  a (x - 2) (x - 8)          and since    (5,3)  is on the graph, we can find "a"  as

 

3  =  a ( 5 - 2) (5 - 8)

 

3  = a (3)(-3)

 

3 = - 9a

 

a =  -1/3

 

So we have that

 

y  = (-1/3) (x - 2) (x - 8)

 

y  = (-1/3) (x^2 - 10x + 16)

 

y = (-1/3)x^2  + (10/3)x  - (16/3)

 

So     a  +  b   +  c   =   (-1/3)  + (10/3)  - (16/3)   =   -7/3

 

 

cool cool cool

 Jul 12, 2019

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