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?

Question

anonymous · Answer

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

anonymous · Answer

oh you dont divide?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

ok i get it thank you!

anonymous · Answer

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

anonymous · Answer

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:
$$(-16)t ^{2}-3t+2.25=-51$$

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

did i doit right then?

amistre64 · Answer

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

amistre64 · Answer

yeah, it looks like you did it good

anonymous · Answer

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

amistre64 · Answer

the final result IS vertex form

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

ik, i need to find h and k now

amistre64 · Answer

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

amistre64 · Answer

forgot to put my ^2 on there :/

anonymous · Answer

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

anonymous · Answer

WAIT IM DONE?

amistre64 · Answer

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

anonymous · Answer

oh i got negative 51...

anonymous · Answer

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?

anonymous · Answer

help...