Question

find the values of a h and k that make the equation
2x^2+8x+4= a(x-h)^2+k

Answer 1

easy way. start with
\[2(x^2+4x)+4\] then
\[2(x+2)^2+\text{stuff}\]

Answer 2

i got the "2" from half of 4. now just go to original equation and replace x by -2 since that will make (x+2)=0 and you will find k

Answer 3

do you mind i have two more questions from this question

Answer 4

\[2(-2)^2+8\times -2+4=8-16+4=-8+4=-4\] and that is your k

Answer 5

could you help?

Answer 6

so answer is
\[2(x+2)^2-4\]

Answer 7

sure just ask

Answer 8

Matrices don't commute to work is ust a little joke, play on words.

Answer 9

btw you can also "complete the square" but this is easier. @estudier i was a little slow on that one

Answer 10

thanks
-3x^2-12x+5= a(x-h)^2+k

Answer 11

ok start with
\[-3(x^2+4x)+5\] and proceed as before

Answer 12

take half of 4 and write
\[-3(x+2)^2+\text{stuff}\]

Answer 13

to find stuff, just replace x by -2 in original expression

Answer 14

since if x = -2 the terms (x+2) is 0

Answer 15

this is quite confusing..

Answer 16

but im sorta getting it.. :s

Answer 17

\[-3(-2)^2-12\times -2+5\]
\[-12+24+5\]
\[12+5\]
\[17\]

Answer 18

hold on one sec

Answer 19

suppose you have
\[y=-3(x+2)^2+k\] is it not clear that if
\[x=-2\] then
\[y=k\]?

Answer 20

kk

Answer 21

because the first term must be 0

Answer 22

and don't forget these are supposed to be the same. that is you are supposed to have
\[-3x^2-12x+5=-3(x+2)^2+k\]

Answer 23

so if i replace x by -2 in the left hand side it is the same as replacing x by -2 in the right hand side

Answer 24

on the right i will get k
on the left i will get whatever number i get, so k must be that number.

Answer 25

and if you do a couple the pattern will be clear. that is replace x by -2 and the first two terms are -12 and +24

Answer 26

it always works this way. double the number of opposite sign

Answer 27

so when i got -12+24+5 i knew it was right. in this case you get 17 so your answer is
\[-3(x+2)^2+17\]

Answer 28

one more... pls..