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The red parabola shown is the graph of the equation $y=ax^2 + bx + c$. Find $a\cdot b\cdot c$.

 Feb 10, 2020
 #1
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The parabola is -1/3*x^2 - 2x + 2, so abc = (-1/3)(-2)(2) = 4/3.

 Feb 10, 2020
 #2
avatar+11731 
+2

The red parabola shown is the graph of the equation $y=ax^2 + bx + c$. Find $a\cdot b\cdot c$.

laugh

 Feb 10, 2020
 #3
avatar+109740 
+1

The vertex  is  (-3, 5)

 

And the x coordinate of the  vertex  is given by

 

-b / [ 2a]  = -3

 

b = 6a

 

And the point  (-1, 3)  is on the graph.....so.....we have this system

 

3  =  a(-1)^2  + 6a (-1)  + c

5  =  a(-3)^2  + 6a(-3)  + c         simplify

 

a  - 6a  + c   = 3

9a  - 18a  + c  = 5

 

-5a  + c   = 3

-9a  + c   = 5          multiply  the second equation through by  -1

 

-5a  + c   = 3

9a   -  c  = -5           add these

 

4a  = -2

a = -2/4  = -1/2  

 

So  b  = 6(-1/2)  =  -3

 

And  -9a  + c  =  5    ....so....

-9(-1/2) + c  = 5

9/2  + c  =10/2

c = 10/2  - 9/2 =   1/2

 

So

 

a  *  b  *  c  =

 

(-1/2) * (-3)  * 1/2  =

 

3 / 4

 

Here's a graph  : https://www.desmos.com/calculator/nl6jcccb3k

 

 

cool cool cool

 Feb 10, 2020
edited by CPhill  Feb 10, 2020

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