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The grid lines in the graph below are one unit apart. The red parabola shown is the graph of the equation y=ax^2+bx+c. Find a+b+c. NOTE: the answer isn’t -3. 

 


 Feb 13, 2020
edited by Guest  Feb 13, 2020
edited by Guest  Feb 13, 2020
 #1
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1. The parabola is y = 1/4*x^2 - 3x + 9, so a + b + c = 1/4 + (-3) + 9 = 25/4.

 

2. The equation of the parabola is y = 2x^2 - 4x + 7, so a + b + c = 5.

 Feb 13, 2020
 #2
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Both answers are incorrect. :/

Guest Feb 13, 2020
 #3
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+1

The vertex  is  ( 2,1)  = (h, k)

 

Note that if we  have the form

 

y = a(x -h)^2 + k         substituting the vertex coordinates into this we have

 

y = a(x - 2)^2  +  1

 

Since  the point  (0, 5)  is on the graph we have that

 

5  = a( 0 - 2)^2  + 1

 

5 = a(-2)^2 + 1

 

4 = 4a

 

a = 1

 

So we have this

 

y = 1 ( x - 2)^2  + 1

 

y = 1x^2 - 4x + 4 + 1

 

y = 1x^2 - 4x + 5

 

a  = 1

b = -4

c =5

 

a + b + c  = 

 

1 - 4 + 5 =

 

2

 

 

cool cool cool

 Feb 13, 2020

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