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avatar+752 

The parabola $y = ax^2 + bx + c$ is graphed below.  Find $a+b+c$.  (The grid lines are one unit apart.)

 

The parabola goes through (-5,0), (0,3), and (4,0).

 Jun 22, 2024
 #1
avatar+129725 
+1

c = 3

 

a(-5)^2 +b(-5)  + 3  = 0

a(4)^2  + b(4) +3  = 0

 

25a - 5b   =  -3   →    100a - 20b  = -12

16a + 4b =  -3   →      80a + 20b = -15

 

180a  = -27

a = -27/180  =  -3/20

 

16 (-3/20) + 4b = -3

4b  = -3 + 48/20

b = -3/4 + 48/80=   -3/20

 

a + b + c = 2 * ( -3/20 ) + 3  =  -6/20 + 60/20  = 54/20  =  27 / 10

 

 

cool cool cool

 Jun 22, 2024

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