please help me
The graphs of f(x) and g(x) are shown below:
graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 9, 0.
If f(x) = (x + 7)2, which of the following is g(x) based on the translation?

- anonymous

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- anonymous

http://broward.flvs.net/webdav/assessment_images/educator_algebraI_v20/segment2_graph33.gif

- Michele_Laino

I'm sorry, I'm not able to see your graphs

- anonymous

@Michele_Laino sorry i had an emergency hold on

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## More answers

- anonymous

@Michele_Laino

##### 1 Attachment

- Michele_Laino

hint:
the graph of f(x), can be obtained from the graph of g(x), making a traslation by 2 units to right

- Michele_Laino

or, vice versa, the graph of g(x), can be obtained from the graph of f(x), making a traslation by2 units to left

- Michele_Laino

the last condition, can be expressed by this formula:
\[\Large g\left( x \right) = f\left( {x + 2} \right)\]

- anonymous

im still sort of confused

- anonymous

If f(x) = (x + 7)2, which of the following is g(x) based on the translation?
g(x) = (x + 9)2
g(x) = (x + 5)2
g(x) = (x − 9)2
g(x) = (x − 5)2
theres are the choice they gave me

- Michele_Laino

in other words, you have to replace x, with x+2 into the expression of f(x), namely:
\[\Large g\left( x \right) = f\left( {x + 2} \right) = {\left( {x + 2 + 7} \right)^2} = ...\]

- anonymous

o ok it said +5 so i was totally confused

- anonymous

ok so i understand it would be A then?

- Michele_Laino

no, sorry I have made a typo

- anonymous

so it isnt A?

- Michele_Laino

yes! correct! it is option A

- anonymous

ok thank you so much can you help with a few more?

- Michele_Laino

ok!

- anonymous

ok 1 sec please

- anonymous

ok im ready
Which graph shows the quadratic function y = 3x2 + 12x + 14?

##### 1 Attachment

- anonymous

@Michele_Laino

- Michele_Laino

your function is a parabola, right?

- anonymous

yes it is

- Michele_Laino

the equation of the axis of your parabola, is:
\[\Large x = - \frac{{12}}{{2 \cdot 3}} = ...\]

- Michele_Laino

which is the x-coordinate of the vertex. please complete:
\[\Large x = - \frac{{12}}{{2 \cdot 3}} = ...?\]

- anonymous

-2?

- Michele_Laino

correct! the equation of the axis of your parabola, is x=-2, furthermore, the x-coordinate of the vertex of your parabola, is also x=-2

- anonymous

so the answer would be graph a because its the only one with negative 2 aas the x coordinate

- anonymous

o nvm it could also be c

- anonymous

but i think it is a

- Michele_Laino

ok! we have to understand what is the right graph:
A or C?

- anonymous

i think a because its at -2,-2

- Michele_Laino

the y-coordinate of your parabola is:
\[\Large y = \frac{{4ac - {b^2}}}{{4a}}\]
where a=3, b=12, and c=14

- Michele_Laino

oops..it is the y-coordinate of the vertex of your parabola

- anonymous

so it is not a?

- Michele_Laino

so after a substitution, we get:
\[\Large y = \frac{{4ac - {b^2}}}{{4a}} = \frac{{4 \cdot 3 \cdot 14 - {{12}^2}}}{{4 \cdot 3}} = ...?\]
please complete

- anonymous

1sec let me do it

- Michele_Laino

ok!

- anonymous

-2 again so it is a

- Michele_Laino

are you sure?
I got a different result

- Michele_Laino

\[\large y = \frac{{4ac - {b^2}}}{{4a}} = \frac{{4 \cdot 3 \cdot 14 - {{12}^2}}}{{4 \cdot 3}} = \frac{{168 - 144}}{{12}} = ...?\]

- anonymous

yes that what i got 168 - 144 i did it wrong its positive 2 but i used thos step

- anonymous

so its c for some reason i added a negtive signat the end of the problem

- Michele_Laino

correct! it is option C

- anonymous

thank you so much

- Michele_Laino

:)

- anonymous

can u help with 1 more

- anonymous

Which of the following represents the factored form of f(x) = x3 − 64x?

- anonymous

@Michele_Laino

- Michele_Laino

ok! I'm here

- anonymous

k can you help me with this 1
Which of the following represents the factored form of f(x) = x3 − 64x?

- Michele_Laino

yes!

- Michele_Laino

first step:
we can factor out x, so we can write this:
\[\Large {x^3} - 64x = x\left( {{x^2} - 64} \right)\]

- Michele_Laino

subsequently, we can use this algebraic identity:
\[\Large {A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right)\]
where A=x, and B= 8

- anonymous

we have to foil this right if so can you show me how i would set it up?

- Michele_Laino

no, it is not necessary to apply the foil method, since we have to apply that standard identity

- Michele_Laino

you should get this:
\[\Large {x^2} - 64 = \left( {x - 8} \right)\left( {x + 8} \right)\]

- anonymous

theses are the choices
f(x) = x(x + 8)(x − 8)
f(x) = (x − 8)(x + 8)
f(x) = x(x − 8)2
f(x) = x(x2 − 8)

- Michele_Laino

so, the complete factorization, is:
\[\Large {x^3} - 64x = x\left( {{x^2} - 64} \right) = x\left( {x - 8} \right)\left( {x + 8} \right)\]

- anonymous

o ok so i just needed to find wat squared equals 64 ok so its b

- Michele_Laino

I think it is option A

- anonymous

o ok you are right i see my error with the x variable

- anonymous

ay thank you so much michele u were really helpfull :) lol and u have a sexy as name

- Michele_Laino

thanks! :)

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