The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.
5(x − 7)2 + 13; The minimum cost to produce the product is $13.
5(x − 7)2 + 13; The minimum cost to produce the product is $7.
5(x − 7)2 + 258; The minimum cost to produce the product is $7.
5(x − 7)2 + 258; The minimum cost to produce the product is $258.

- anonymous

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- anonymous

@Nnesha

- Nnesha

Hey, do you know how to `complete the square` ?

- anonymous

Barley

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## More answers

- Nnesha

oh alright
\[\huge\rm f(x)= 5x^2 − 70x + 258 \]
this is our equation where a b ,c values are \[\rm Ax^2+Bx+C=0\]
a=leading coefficient
b=middle term
c=constant term
we need to complete the square of (5x^2+70x) \[(5x^2+70x)+258\]

- Nnesha

first of all take out the common factor from (5x^2+70x) what is common factor(just common number not varaible ) ?

- anonymous

2?

- Nnesha

nope

- Nnesha

\[\huge\rm \color{Red}{5}x^2+\color{reD}{70}x\]
5 isn't divisible by 2

- anonymous

Oh, sorry, I mixed that up with something else. So, then what 5?

- Nnesha

yes right take out the 5 from both terms 5x^2 and 70x\[5(??+??)\]

- anonymous

would you divide 70 by 5?

- Nnesha

when you take out 5 from 5 what would you get ?

- anonymous

0

- Nnesha

in other words divide both terms by common factor |dw:1441211901863:dw|
what do you get when yo udivide 5 x^2 by 5
and 70x/5 = ? write ur answer in the parentheses

- anonymous

5(x^2 +14)+258?

- Nnesha

yes right!!

- Nnesha

wait you forgot x

- Nnesha

\(\color{blue}{\text{Originally Posted by}}\) @gigirained
5(x^2 +14)+258?
\(\color{blue}{\text{End of Quote}}\)
5(x^2 +14x)+258
like this

- anonymous

Oh alright

- Nnesha

now to complete the square
divide b/2 and then take square of (b/2)^2

- Nnesha

i'll give you an example \[\huge\rm x^2+Bx+C=0\]
\[\rm (x +\frac{ b }{ 2})^2 -(\frac{ b }{ 2})^2+C=0\]
like this
b = middle term

- Nnesha

what's the middle term in that equation ?

- anonymous

14?

- Nnesha

yes right divide 14 by 2 then take square root of the result

- Nnesha

\[\huge\rm 5(x-\frac{ 14 }{ 2 })^2-(\frac{ 14 }{ 2 })^2 +258\]

- anonymous

5(x-7)^2 - 7^2 +258

- Nnesha

i just noticed it supposed to be negative 14x
cux in the original equation 70x is negative

- anonymous

Okay

- Nnesha

yes right!
7^2 = ?

- anonymous

49

- anonymous

do we do anything with 258?

- Nnesha

hmm wait

- Nnesha

ohh yeah we have common factor we have to multiply (b/2)^2 with 5

- Nnesha

\[\huge\rm \color{Red}{5}(x-7)^2-[(7)^2\times \color{ReD}{5}] +258\]we should multiply (b/2)^2 wth the common factor

- anonymous

would we multiply 7 by 5 for 49 by 5

- Nnesha

first take square of 7 then multiply by 5

- anonymous

245

- Nnesha

yes right now combine like terms \[5(x-7)^2\color{Red}{-245+258}\]

- anonymous

5(x-7)^2 + 13

- Nnesha

then you will get vertex form equation of parabola \[\huge\rm y=a(x-h)^2+k\]
where (h,k) is the vertex
if a is positive then you wll get minimum point (h,k)
if a is negative you will get maximum point (h,k)
(h,k) where h represents x-coordinate
and k represents y -coordinate
cost usually represents by y -coordinate

- Nnesha

yes right

- Nnesha

done!

- anonymous

So, i dont know which one, A or B @Nnesha

- Nnesha

reread my my comment again
which coordinate represent cost ?

- Nnesha

what's the vertex point ?

- anonymous

7

- anonymous

well, the answer i got was b

- Nnesha

that's one h
what is k ?

- anonymous

13

- anonymous

?

- Nnesha

yes right (h,k) = (7,13)
where y -coordinate represent cost

- anonymous

how do i find the y-coordinate

- Nnesha

(x,y) is same as (h,k)
first number is x-coordinate 2nd one is y-coordinate

- anonymous

oh lol never mind

- anonymous

That went right over my head haha

- Nnesha

in other words k represent cost in this question

- anonymous

Thank you so much!

- Nnesha

np :)

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