Mathematics
OpenStudy (anonymous):

Y=-16t^2+48t+15. Write in vertex form,I don't know why, but my algebra teacher said to divide all the numbers by 16, EXCEPT 15. Any help?

OpenStudy (anonymous):

you have to bring the 15 over to the other side first, THEN factor out the -16

OpenStudy (anonymous):

oh you dont divide?

OpenStudy (anonymous):

y - 15 = -16(t^2 - 3t) then...

OpenStudy (anonymous):

you have to make that binomial in the parentheses a perfect square trinomial, to do this we take .5 the b term and square it, so .5 of -3 is 1.5, then that squared is our new c term which is 2.25

OpenStudy (anonymous):

i know that but i was just confused on why you don't divide?

OpenStudy (anonymous):

then we take the new c term multiplied by the number we factored out (-16) and put that number on the other side (do not do reverse operations here, if it is negative, you subtract not add). So 2.25 x -16 is -36. So the new y - 15 is now y - 15 - 36 or y - 51

OpenStudy (anonymous):

you dont divide in this, you just factor out the 'a' term, it is like division, but we do not get rid of it

OpenStudy (anonymous):

ok i get it thank you!

OpenStudy (anonymous):

You're welcome, if you need any more help just let me know.

OpenStudy (anonymous):

ok i understand that you have to multiply by -16 and why, but won't that affect the perfect trinomial? or will it turn into: $(-16)t ^{2}-3t+2.25=-51$

OpenStudy (amistre64):

you dont need to factor out all the numbers, just the t values will do

OpenStudy (amistre64):

$y=-16t^2+48t+15$ $y=(-16t^2+48t)+15$ $y=-16(t^2-3t)+15$

OpenStudy (amistre64):

the rest of it is completing the square on your t parts

OpenStudy (anonymous):

did i doit right then?

OpenStudy (amistre64):

hmm, (3/2)^2 = 9/4 sooo..... $y=-16(t^2-3t+\frac{9}{4})-(-16)(\frac{9}{4})+15$ $y=-16(t-\frac{3}{2})^2+36+15$ $y=-16(t-\frac{3}{2})^2+51$

OpenStudy (amistre64):

yeah, it looks like you did it good

OpenStudy (anonymous):

yay, ok so how would i turn this in to vertex form?

OpenStudy (amistre64):

the final result IS vertex form

OpenStudy (anonymous):

but i thought you would just get a "plus or minus this" answer

OpenStudy (amistre64):

thats not vertex, that +- stuff is solving for the roots

OpenStudy (amistre64):

vertex form is the equation using the vertex as a part of the equation

OpenStudy (anonymous):

ik, i need to find h and k now

OpenStudy (amistre64):

$y=a(x-h)^2+k$ $y=-16(x-\frac{3}{2})+51$

OpenStudy (amistre64):

forgot to put my ^2 on there :/

OpenStudy (anonymous):

yes i have this so far, so now would i square root everything?

OpenStudy (anonymous):

WAIT IM DONE?

OpenStudy (amistre64):

.... its always best that when you get to the end, to stop lol

OpenStudy (anonymous):

oh i got negative 51...

OpenStudy (anonymous):

don't you subtract 15, which turns it negative, and then you take half of -3 and square it which is 2.25. 2.25 times -16 is -36. Don't you then add 36 to negative 15 and get 21?

OpenStudy (anonymous):

help...