## anonymous 5 years ago 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?

1. anonymous

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

2. anonymous

oh you dont divide?

3. anonymous

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

4. 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

5. anonymous

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

6. 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

7. 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

8. anonymous

ok i get it thank you!

9. anonymous

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

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

11. amistre64

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

12. amistre64

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

13. amistre64

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

14. anonymous

did i doit right then?

15. amistre64

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

16. amistre64

yeah, it looks like you did it good

17. anonymous

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

18. amistre64

the final result IS vertex form

19. anonymous

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

20. amistre64

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

21. amistre64

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

22. anonymous

ik, i need to find h and k now

23. amistre64

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

24. amistre64

forgot to put my ^2 on there :/

25. anonymous

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

26. anonymous

WAIT IM DONE?

27. amistre64

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

28. anonymous

oh i got negative 51...

29. 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?

30. anonymous

help...