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

 

 Jun 30, 2020
 #1
avatar+21955 
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Using the graphing equation:  y  =  a(x - h)2 + k     where  (h, k) is the vertex.

 

The vertex of this parabola occurs at  (2, 1)     --->     y  =  a(x - 2)2 + 1

 

It rises, so that the value of a is positive.

It has no stretching or contracting so the value of a is 1.

 

The equation is:  y  =  1(x - 2)2 + 1     or     y  =  (x - 2)2 + 1.

 

Now, multiply this out and simplify ... 

 Jun 30, 2020
 #2
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I'm still stuck. Can you explain farther?

 Jun 30, 2020
 #3
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Anyone?

 Jul 1, 2020
 #4
avatar+31087 
+1

Notice that the curve goes through the following three points (you could choose any three, but these are easy ones):

 (0, 5)   (2, 1)  and  (4, 5)

 

This allows you to set up the following three equations:

 

5 = a*02  +  b*0 + c     or simply  c = 5

 

1 = a*12 + b*1 + c     or   a + b = -4         ...(1)

 

5 = a*42 + b*4 + c    or    16a + 4b = 0    ...(2)

 

You could solve equations (1) and (2) for a and b if you wish; however, since you are only asked for a + b + c you could simply use the value of a + b from (1) together with the value for c.

 Jul 1, 2020
 #5
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But 1 isn't right!

 Jul 1, 2020
 #6
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the answer is 2

 Jul 1, 2020

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