Question

okay so i was gone this day and have no clue what to do or anything so please help again....Determine a and k so the given points are on the graph of the function (1,7)(2,-23) ; y=a(x+1)^2+k

Answer 1

ok here is the deal, we go slow.
replace x by 1, set the result = 7 and write
\[a(1+1)^2+k=7\]
\[2a+k=7\]

Answer 2

omg satellit73 i feel stupid thanks so much for all your help seriously.

Answer 3

then repeat with x = 2 and result = -23 to get
\[a(2+1)^2+k=-23\]
\[9a+k=-23\] so far so good?

Answer 4

no problem, we take it step by step

Answer 5

yes this is helping
keep going please

Answer 6

so now we have two equations involving a and k

\[2a+k=7\]
\[9a+k=-23\] and we want "a" and "k"

Answer 7

except i made a mistake, because
\[1+1=2\] and
\[2^2=4\] so the first one should be
\[a(1+1)^2+k=7\]
\[4a+k=7\] my fault sorry about that.

Answer 8

its ok

Answer 9

so we still have two equations
\[9a+k=-23\]
\[4a+k=7\] and so we can subtract the second one from the first to get one equation with one variable

Answer 10

we will get by subtraction
\[5a=-30\] and therefore
\[a=-6\]

Answer 11

now since we know
\[a=-6\] we can substitute into either equation and solve for k. we can write
\[4\times (-6)+k=7\]
\[-24+k=7\]
\[k=31\] i think that should work

Answer 12

so basically the bigger of the two will go on top?

Answer 13

it makes no difference really which one is larger. by larger i assume you mean the coefficient of the "a" term. we could have written
\[4a+k=7\]
\[9a+k=-23\] and subtracted to get
\[-5a=30\] and still
\[a=-6\] i just like working with positive coefficients to make life a tiny bit simpler

Answer 14

i dont see where k=31 where the 31 comes from?

Answer 15

ok lets go slow again. we agree that
\[a=-6\] right?

Answer 16

yes

Answer 17

and we also know that
\[4a+k=7\] yes?

Answer 18

si

Answer 19

and since
\[a=-6\] this tells us that
\[4\times (-6)+k=7\] by substituting -6 for "a"
so we know
\[-24+k=7\] and we can solve for k by adding 24 to both sides to get
\[k=7+24\]
\[k=31\]

Answer 20

ahhhhh haaa okay i get it haha sorry

Answer 21

no need for sorry, this is confusing because you have to remember how to solve a system of equations to do this seemingly unrelated problem

Answer 22

THANK YOU SOOOOO MUCH IM SORRY IT SUCKS BEING GONE AND HAVING A TEST DO AT MIDNIGHT THAT HE DIDNT TELL ME ABOUT.

Answer 23

so your "final answer" is
\[y=-6(x+1)^2+31\] ad we can check that this is right if you like

Answer 24

THANK YOU THANK YOU THANK YOU HAHA ITS RIGHT :):):)

Answer 25

how do you have a test at midnight?

Answer 26

on line school for night owls?

Answer 27

DUE AT MIDNIGHT
HE GAVE US A TAKE HOME TEST ONLINE

Answer 28

nice. any more feel free to post

Answer 29

I GO TO A HIGH SCHOOL THAT GAVE ALL STUDENTS THEIR OWN LABTOPS AND SO OUR CLASS ASSIGNMENTS AND TEST AND QUIZES ARE ALL ONLINE BUT HE TEACHES US OFFLINE.
HE'S NOT A VERY GOOD TEACHER....THIS ISNT ACTUALLY KAITLYN EITHER ITS HER FRIEND BUT OCCASIONALLY SHE LETS ME USE THIS!