+0  
 
0
118
4
avatar+139 

The red parabola shown is the graph of the equation \(x = ay^2 + by + c\). Find \(a + b + c\).



Each tick mark on the graph is one unit.

 Nov 27, 2020
 #1
avatar
+1

Start with the vertex  5,-4

   vertex form x=   a (y+4)^2 +5     use point  (3,-2)   to calc  a =  - 1/2

 

x = -1/2 (y+4)^2 + 5

 Nov 27, 2020
 #2
avatar
+1

...then expand to    x = (-1/2)(y^2+8y+16) +5

                               x = -1/2y^2 -4y-3     take it from here   

Guest Nov 27, 2020
 #3
avatar+116126 
+1

We have the form

 

x  = - a ( y - k)^2  +  h 

 

And the vertex  =  (5, -4) = (h, k)

 

x =  -a ( y - - 4)^2  + 5

 

x = -a  ( y + 4)^2  +   5

 

We know another point on the  graph  ( -3, 0)

 

So....we can solve for  a

 

-3  = -a ( 0 + 4)^2  + 5

 

-3 - 5 =  -a ( 16)

 

-8 = -a (16)

 

-8/-16 = a

 

1/2  = a

 

So we have

 

 

x = (-1/2) ( y + 4)^2  +  5     expand this

 

x= (-1/2) ( y^2  + 8y + 16)  + 5

 

x = (-1/2)y^2  -4y  -8 + 5

 

x = (-1/2)y^2 - 4y -3

 

a  +  b  +  c  =   (-1/2)  - 4 - 3  =   -7 1/2   =    - 15/2

 

Here's a graph :  https://www.desmos.com/calculator/fxczjujb5g

 

 

cool cool cool

 Nov 27, 2020
 #4
avatar+139 
+1

woah thanks that was a lot

 Nov 27, 2020

60 Online Users

avatar
avatar
avatar