anonymous
  • 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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
you have to bring the 15 over to the other side first, THEN factor out the -16
anonymous
  • anonymous
oh you dont divide?
anonymous
  • anonymous
y - 15 = -16(t^2 - 3t) then...

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anonymous
  • 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
anonymous
  • anonymous
i know that but i was just confused on why you don't divide?
anonymous
  • 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
anonymous
  • 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
anonymous
  • anonymous
ok i get it thank you!
anonymous
  • anonymous
You're welcome, if you need any more help just let me know.
anonymous
  • 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: \[(-16)t ^{2}-3t+2.25=-51\]
amistre64
  • amistre64
you dont need to factor out all the numbers, just the t values will do
amistre64
  • amistre64
\[y=-16t^2+48t+15\] \[y=(-16t^2+48t)+15\] \[y=-16(t^2-3t)+15\]
amistre64
  • amistre64
the rest of it is completing the square on your t parts
anonymous
  • anonymous
did i doit right then?
amistre64
  • amistre64
hmm, (3/2)^2 = 9/4 sooo..... \[y=-16(t^2-3t+\frac{9}{4})-(-16)(\frac{9}{4})+15\] \[y=-16(t-\frac{3}{2})^2+36+15\] \[y=-16(t-\frac{3}{2})^2+51\]
amistre64
  • amistre64
yeah, it looks like you did it good
anonymous
  • anonymous
yay, ok so how would i turn this in to vertex form?
amistre64
  • amistre64
the final result IS vertex form
anonymous
  • anonymous
but i thought you would just get a "plus or minus this" answer
amistre64
  • amistre64
thats not vertex, that +- stuff is solving for the roots
amistre64
  • amistre64
vertex form is the equation using the vertex as a part of the equation
anonymous
  • anonymous
ik, i need to find h and k now
amistre64
  • amistre64
\[y=a(x-h)^2+k\] \[y=-16(x-\frac{3}{2})+51\]
amistre64
  • amistre64
forgot to put my ^2 on there :/
anonymous
  • anonymous
yes i have this so far, so now would i square root everything?
anonymous
  • anonymous
WAIT IM DONE?
amistre64
  • amistre64
.... its always best that when you get to the end, to stop lol
anonymous
  • anonymous
oh i got negative 51...
anonymous
  • 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?
anonymous
  • anonymous
help...

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