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The graph of $y=ax^2+bx+c$ is shown below. Find abc. (The distance between the grid lines is one unit.)

 Jun 12, 2021
 #1
avatar+179 
+1

Since the graph passes through (-3, -2), (-1, 0), and (-5, 0), we have the equations \(9a-3b+c = -2, a-b+c = 0,\) and \(25a-5b+c= 0\).  Solving, we have a = 1/2, b = 3, c = 5/2, which means that abc = 15/4

 Jun 12, 2021
 #2
avatar+35059 
+2

Parabola with vertex  -3,-2

Vertex form     y = a (x+3)^2 - 2        choose point (-1,0)    when x = -1    y = 0   shows a = 1/2

 

y = 1/2 (x+3)^2 -2    expand

y = 1/2 x^2 +3x + 2.5                    1/2   x 3  x 2.5 = 3.75      ( as EL found via a different method !)

 Jun 12, 2021

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