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

 

 Apr 23, 2024
 #1
avatar+128776 
+1

The vertex is  ( 3,1)  and the points  (0,7) and (6,7) are on the graph

 

c = 7

 

 

1 = a (3)^2  + b(3) + 7

7 = a(6)^2 + b(6) + 7            simplify

 

9a + 3b =  - 6    →  3a + b = -2 →   b = -2 - 3a     (1)

36a + 6b =  0       (2)

 

Sub (1)  into (2)

 

36 a + 6(-2-3a)  = 0

 

36a - 12 - 18a  =  0

 

18a =  12

 

a = 2/3

 

b = -2  - 3(2/3)  =  -2 - 2 =  -4

 

a * b * c =    (2/3) * (-4) * 7   =   -56 / 3

 

cool cool cool

 Apr 23, 2024

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