Melody

Hi Solveit  :))

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)

\(y=ax^2+bx-6a\)

     \(\frac{-b}{2a}=-3\\ -b=2a*-3\\ -b=-6a\\ b=6a\\ \mbox{so the equation becomes}\\ y=ax^2+6ax-6a\\ y=a(x^2+6x-6) \)

If x=0 then 

y=a(-6) <0     so      (0,3) CANNOT be a point but  (0,-3) could be

If x=-3

y=a(9-18-6) <0    so    (-3,0) CANNOT be a point but (-3,-3) could be

If x=+3

y=a(9+18-6)>0   so  (3,3) can be a point

SO

(0,3) and (-3,0)   cannot be points on the parabola.

I do not remember ever hearing the word "radicand" before   ://

I just looked it up. :D

\(\sqrt{x}-4 \qquad \mbox{Radicand is x}\\~\\ \sqrt{x-4} \qquad \mbox{Radicand is } (x-4)\\~\\\)

Hayley, you could have said a little more than that I think!     

No real number times by itself can give a negative answer, therefore   sqrt(-81)  has no real solution.

-3-6(-4k+5)=-12+3k

\(-3\;\;\;\:\qquad -6(-4k+5)=-12+3k\\ -3+12\;\;\;-6(-4k+5)=-12+3k+12\\ 9\;\;\;-6(-4k+5)=+3k\\ \mbox{divide both sides by 3}\\ 3\;\;\;-2(-4k+5)=+1k\\ 3\;\;\;+8k-10=+1k\\ 8k-7=k\\ 7k=7\\ k=1\)

         f(2x)=[f(x)]^2

Given the equation above, if f(1)=3, what is f(2) ?

\(f(2x)=[f(x)]^2\\~\\ f(1)=3\\~\\ f(2*1)=[f(1)]^2\\~\\ f(2)=[f(1)]^2\\~\\ f(2)=[3]^2\\~\\ f(2)=9\)

Thanks kids, I did enjoy reading this thread :)

Yes, of course Hayley.  !!

Attn: Hayley1 and others   

Ok you kids have got some concept problems here.

MULTIPLES

A multiple of a number is bigger to or equal to the number.

Multiples of 12 are 12, 24, 36, 48, 60, 72,  ........., 120      ....

Multiples of 15 are 15, 30, 45, 60, 75, 90,  .....,      120,     ....

The common multiples are the ones that are common to both lists.  that is  60,  120,  180, .......

The LEAST common multiple is  60  because that is the smallest common multiple.  It is the one with the LEAST value.  

-----------------------------------------------------

FACTORS

The factors of 12 are   1, 2, 3, 4, 6, 12

The factors of  15 are  1, 3, 5, 15

So the HIGHEST common factor of 12 and 15 is 3 

Thanks Guys   (in Australia guys used like this always includes the girls )

This will give you a very concise history of the forum :)

Fri  11/12/15

1)   Riddle   Thanks DragonSlayer554

      https://web2.0calc.com/questions/riddle_3

2)   Why do I keep being flagged?     Thanks Nauseated

      https://web2.0calc.com/questions/wht-do-i-do-without-being-flagged#r3

3)   Prime factorization   Thanks Hayley1 and The4knaves    

      https://web2.0calc.com/questions/help_20777#r2

4)   Factors and Multiples    Melody

      https://web2.0calc.com/questions/math-is-coool-yyyyyyyyyyyyyyyyeeeeeeeeeeeeeeeesssssssssssssss#r6

5)   Function Notation question  (strange but not too hard)    Melody

      https://web2.0calc.com/questions/help_88901#r5

6)   Which points cannot be on the parabola     Melody

      https://web2.0calc.com/questions/little-help

7)   Is this a growth function     Heureka

      https://web2.0calc.com/questions/is-it-f-x-3-5-3-x-a-exponential-growth-function