+0  
 
0
10
2
avatar+1037 

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 (-3,7), (-1,5), and (2,8).

 Jan 12, 2024
 #1
avatar+36916 
+1

Much easier to answer this if we had the graph to which the post refers.... frown

 Jan 12, 2024
 #2
avatar+128408 
+1

We can solve these equations

 

7 = a (-3)^2  + b(-3)  +  c

5 = a(-1)^2   + b(-1) +  c

8 = a(2)^2    + b(2)  +  c

 

Simplify  as

 

9a - 3b + c   =  7         (1)

a  - b  + c  =  5        (2)

4a + 2b + c  =  8         (3)

 

Multiply  (2)  by -3 and add to (1)

6a - 2c  = -8   →   3a - c  = -4    (3)

 

Multiply  (2) by 2  and add to (3)

6a  + 3c  = 18   → 2a + c = 6     (4)

 

Add (3)  and (4)

 

5a = 2

a = 2/5

 

To find c

2(2/5) + c =  6

4/5 + c  = 6

c = 6 -4/5   =  26/5

 

To find b

2/5  - b + 26/5 =  5

b  =  2/5 + 26/5 - 25/5

b = 3/5

 

a + b +  c  =   

 

2/5 + 3/5 + 26/5    =

 

31 / 5

 

 

cool cool cool

 Jan 12, 2024

3 Online Users

avatar
avatar