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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.)   

 

 Dec 6, 2021
 #1
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When x = 0, y = 7  so   7 = a*0^2 + b*0 + c

 

When x = 3, y = 1, so   1 = a*3^2 + b*3 + c

 

When x = 6, y = 7, so   7 = a*6^2 + b*6 + c

 

You now have three simultaneous equations for the three unknowns.  I'll leave you to solve them.

 Dec 6, 2021
 #2
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Vertex form of parabola with   vertex  ( 3,1)

 

y = a ( x-3)^2  + 1        when x = 0    y = 7      then 'a' = 7/10

 

y = 7/10 (x-3)^2 + 1      expand to find a , b  and c     

 Dec 6, 2021

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