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The grid lines in the graph below are one unit apart. The red parabola shown is the graph of the equation $y = ax^2 + bx + c.$ Find $a+b+c$. 

https://latex.artofproblemsolving.com/c/e/2/ce264d13e5e7038f82ba3bae952d91fdf182b0ff.png

 Feb 16, 2018
 #1
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The y intercept is (0, 5)....so  "c"  = 5

 

The vertex  is  (2,1)

 

The coordinate of the vertex  is

 

-b/[ 2a ]  =  2

-b = 4a

b = - 4a

 

And (1,2)  is on the graph....so we have that

 

2  =  a(1)^2  - 4a(1)  + 5

2  = a  - 4a  + 5

-3  = -3a

1  =  a

 

So   b = -4(1)  =  -4

 

a + b + c   =   1 - 4  + 5    =  2

 

 

cool cool cool

 Feb 16, 2018

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