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Help with parabolas

 

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

 

The parabola passes through (-2,8), (0,0), and (2,8).

 Dec 17, 2023
 #1
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We can use the three given points to solve for the equation's coefficients a, b, and c:

 

1. Substitute point (-2, 8):

8 = 4a - 2b + c

 

2. Substitute point (0, 0):

0 = 0a + 0b + c

 

3. Substitute point (2, 8):

8 = 4a + 2b + c

 

Now we have three equations and three unknowns. We can solve the system of equations to find a, b, and c:

From equation 2, we can see that c = 0.

 

Substitute c = 0 into equations 1 and 3:

8 = 4a - 2b

8 = 4a + 2b

 

Add the two equations: 16 = 8a, so a = 2.

 

Substitute a = 2 back into either equation 1 or 3:

8 = 8 - 2b, so b = -4.

 

Therefore, a + b + c = 2 - 4 + 0 = -2.

 

So, the answer is -2.

 Dec 17, 2023

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