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\(\text{A parabola with equation $y=ax^2+bx+c$ contains the points $(-3,3)$, $(1,3)$, and $(0,0)$. Find the value $100a+10b+c$. }\)

 

Thanks! smiley

 Jul 17, 2019
 #1
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If (0,0)  is on the graph, then c  = 0

 

So.....we have these two equations

 

a(-3)^2 + b(-3)  =  3    ⇒ 9a - 3b  = 3      (1)

a(1)^2 + b(1)  =    3   ⇒ a  + b  = 3  ⇒  3a + 3b =  9     (2)

 

Add (1)  and (2)   and we have that  

 

12a  =  12

a  = 1

 

And using (1)

9)1) - 3(b)  = 3

9 - 3b  = 3

-3b  = -6

b  = 2

 

So   100a  + 10b + c   =    100(1) + 10(2) + 0   =   100 + 20 =  120

 

 

cool cool cool

 Jul 17, 2019

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