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The function g is defined as g(x)=ax^2+bx-6a, where a and b are positive constants. The function has a line of symmetry at x=-3. Which of the following could NOT be a coordinate pair on the graph of y=g(x)?

A) (0,-3)

B) (0,3) 

C) (-3,0)

D) (3,3)

E) (-3,-3)

 Dec 10, 2015

Best Answer 

 #2
avatar+118587 
+5

You have done it again Solveit !!

 

I just answered an earlier posting of this same question.

You must state they are reposts and send people to the original thread.

I know you have only done this because you did not know what you were supposed to do.

I have been watching you and I know you have beatiful manners. :)

 Dec 11, 2015
 #1
avatar+128079 
+10

The vertex must be at x = -3......

 

And the form would be :

 

y = a(x +3)^2  - 15a   =      ax^2  + 6ax  + 9a  - 15a  =     ax^2 + 6ax - 6a.......and since a is positive, let 6a  = b   so b is also positive......so  the final form is

 

y = ax^2 + bx - 6a   =   ax^2 + 6ax - 6a

 

A) Notice that (0, -3)   could   be on the graph if a = 1/2....

 

B) (0,3) cannot be on the graph because  "a" would have to be -1/2.... but "a" is positive

 

C) (-3, 0)  ...we must have  0  = 9a - 18a  - 6a.....and "a" would have to be 0.....again.....this isn't possible  because  "a"  is positive

 

D) (3,3)   .....we must have 3 = 9a + 18a - 6a  →   3 = 21a  →   a = 1/7  .....so this point could exist

 

E)  (-3, -3).......we must have  -3 = 9a - 18a - 6a  → -3  = -15a    →  a  = 1/5....so this point could exist

 

In summary (A),   (D)  and (E)   are  possible, but (B) and  (C)  are not

 

Here's a graph of the possibilites.......https://www.desmos.com/calculator/rsqelub4qd

 

 

cool cool cool

 Dec 11, 2015
 #2
avatar+118587 
+5
Best Answer

You have done it again Solveit !!

 

I just answered an earlier posting of this same question.

You must state they are reposts and send people to the original thread.

I know you have only done this because you did not know what you were supposed to do.

I have been watching you and I know you have beatiful manners. :)

Melody Dec 11, 2015
 #3
avatar+2498 
0

Thanks CPhill ! :)

 Dec 11, 2015
 #4
avatar+2498 
0

but there is no two answers, teacher said that parabola can be inverted and it means that it can be C (-3,0)  :D

 Dec 11, 2015

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