Question

How do you find k in this expression -4x^2+24x+20 can be written as a(x+h)^2+k

Answer 1

you have to rewrite the left to math the form

Answer 2

match the form that is :)

Answer 3

could you show me how to do this problem please?

Answer 4

-4x^2 +24x +20 ;factor out a -4, a = -4

-4(x^2 -6x -5) ; now complete the square for the innards to set the problem

Answer 5

-4((x^2 -6x +9) -9 -5) ; combine like terms and compress the square

-4((x-3)^2-14) ; distribute the -4 back into it now

-4(x-3)^2 -4(-14)

-4(x-3)^2 +56

Answer 6

so k is 56??

Answer 7

is it in the right place? if so, dbl chk my work to make sure I dint mess up :)

Answer 8

what is in the right place? I really need a step by step on how to do this type of problem. I would really, really appreciate if you could help me with this.

Answer 9

I just gave you a step by step the best way i know how. Other than trying to teach you how to do math all over again, this is the best I can give you for free...

Answer 10

the hardest part is know how to "complete a square" ; which sounds really complex and all, but it really geometry

Answer 11

want easy way to find k?

Answer 12

without completing any square

Answer 13

find the second coordinate of the vertex using
\[-\frac{b}{2a}\] as x
that will be k

Answer 14

just thought i would mention it

Answer 15

-4(x^2 -6x -5) ; now complete the square for the innards to set the problem

focus on the innards: (x^2 -6x -5) we want to transform this into something we can use

if we had an x^2 ; and 6 more of them we can align it up as:

\begin{array}c x^2&x&x&x\\x\\x\\x\end{array}

now to complete the square, how many spots do we need to fill in?

\begin{array}c x^2&x&x&x\\x&1&2&3\\x&4&5&6\\x&7&8&9\end{array}

add 9 to complete the square.

x^2 +6x +9 is a complete square.

BUT, we dont want to simply add 9 to the expression becasue that trows the whole thing out of whack. If we are going to add 9; we also have to subtract 9

(x^2 +6x +9) -9 -5 will keep us on the right track

Answer 16

I mixed -6 and +6, but the same thing applies :)

Answer 17

;yikes not to disagree with amistre but all you have to do is write
\[-4(x^2-6x)+20\]
\[-4(x-3)^2+k\] and you find k by replacing x in the original expression by 3

Answer 18

lol .... thats not a disagreeance, its just a simplification of the process :)

Answer 19

and if the 3 is not obvious use
\[-\frac{b}{2a}\]

Answer 20

abstract algebra is great and all; but its called abstract for a reason ;)

Answer 21

what mathmatical procedure would you recommend for simply stating:

(x^2 -6x) is rewritten as (x-3)^2 ? that doesnt imply alot of arm waving :)