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