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Cheyenne10.22
Group Title
A sandbag was thrown downward from a building. The function f(t)=16t^232t+384 shows the height f(t), in feet, of the sandbag after t sec;
Part A: factor the function f(t) and use the factors to interpret the meaning of the x intercept of the function
 one month ago
 one month ago
Cheyenne10.22 Group Title
A sandbag was thrown downward from a building. The function f(t)=16t^232t+384 shows the height f(t), in feet, of the sandbag after t sec; Part A: factor the function f(t) and use the factors to interpret the meaning of the x intercept of the function
 one month ago
 one month ago

This Question is Closed

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Are you having trouble factoring?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
f(t)=at^2+bt+c if f is factorable, you should be able to find two integer numbers that when multiplied give you a product of a*c and a when added give you a product of b.
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
I don't think I understand it. I came up with (8, 320) for first part but not sure if right and I don't understand second part
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Part A: Says to factor to get the xintercepts. Did you factor yet?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
I think I did it wrong thats where I got a( (8, 320)
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
(8,320) doesn't lay on the xaxis points that lay on the axis are points in the form (a,0) where a is any number notice the y is 0 that means we don't go up and or down from the xaxis and that we are actually on the xaxis The part of the graph that crosses the xaxis is called the xintercept. (You can have more than one) (8,320) does not have the y being 0 so it is definitely not on the xaxis
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
Ok so how factor the function?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
I will copy what I said before: f(t)=at^2+bt+c if f is factorable, you should be able to find two integer numbers that when multiplied give you a product of a*c and a when added give you a product of b.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Can you identify a,b, and c?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
a would be 16, b would be 32, and 384 is c, right?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
I think you had some negative numbers. I know they aren't all positive.
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
sorry 16 and 32 were negative
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so a=16, b=32, and c=384 now recalling my quote from earlier: "f(t)=at^2+bt+c if f is factorable, you should be able to find two integer numbers that when multiplied give you a product of a*c and a when added give you a product of b. " We need to find what a*c is. Then we need to find two integer numbers that have product a*c and also have sum b.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
You could try to make life easier and see if 16, 32,384 have a common factor (greater than one)?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
ok Im trying to find that now. Ok hold on
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Though you could do this with the bigger numbers.
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
the gcf is 16
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
16
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
cool so lets see what happens when we factor 16 out from 16t^232t+384
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[16(\frac{16t^2}{16}\frac{32t}{16}+\frac{384}{16})\]
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so 16/16=? and 32/16=? and 384/16=?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
16/16=1 32/16=2 384/16=24
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so therefore you are saying we have \[16(t^2+2t24)\] Which I totally agree with So instead of looking at those really huge numbers let's reidentify what is a, b, and c We are now just looking at \[t^2+2t24\]
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
So that is the answer for A, but for the second part of the question how do I use that to interpret the xintercept.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
We aren't done factoring.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
I'm asking you to reidentify a,b,and c.
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
oh ok sorry. as you may can tell math isnt my best subject
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
we need to find a*c after. Then we need to find two factors of a*c that have product ac and sum b.
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
a= t^2 b= 2t c= 24 right
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
a,b, and c are the constant values that are in front of the variable squared, in front of the variable, and then lastly the constant not attach to a variable respectively in other words a is the coefficient of t^2 b is the coefficient of t c is the left over term (the constant term)
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
we have at^2+bt+c and we are comparing this to t^2+2t24 now since 1*k=k for all k then 1*t^2=t^2 so you could say we are comparing at^2+bt+c to 1t^2+2t24 if you think that makes it easier
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
Im so confused. wouldn't the factor be 16(t+1624)
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Where did you get 16(t+1624) I thought we had 16(t^2+2t24)
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
I'm not sure. was trying to factor I think I just put the wrong number in.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
ok so we are looking at factoring t^2+2t24 which is the samething as saying 1t^2+2t24 what is a,b, and c? remember you are comparing 1t^2+2t24 to at^2+bt+c to determine what a,b, and c are.
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
a=1t^2 b=2t c=24
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
again a,b, and c are suppose to be constants c is right but a and b for some reason you are inputting the variable part
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
a=1 b=2 c=24 now what is a*c
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
Oh sorry 24
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
ok so since a=1 we can use a shortcut to the factoring style mentioned earlier what are two numbers that multiplied to be 24 and add up to be 2?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
24 and 1
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so 24+(1)=2?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
i thought that was a 7. Im lost again
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
which one of these is true: 24+(1)=2 24+1=2 12+(2)=2 12+2=2 6+4=2 6+(4)=2 8+(3)=2 8+3=2
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
6+(4)=2
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
can you tell what we were looking for?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
i actually told you what we were looking for.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
and where are you lost? I haven't see any 7's yet
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
it was the ? no 7 We were getting the b and c right
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
My thing want copy and paste. But I asked you to find two numbers that multiplied to be 24 and add up to be 2? Can you tell me what two integer numbers do this?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
6 and 4
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so again since a=1 we don't have to go through the longer process which requires factor by grouping so since a=1, t^2+2t24=(t+6)(t4) so we started with f(t)=16t^232t+384 and then we factor f and got f(t)=16(t+6)(t4)
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
Ok Got it.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
You may want to work on more factoring.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
So what are the xintercepts?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
Yes I do. the 6 and 4 right
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
yes I do. the 6 and 4 right
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
4 is right but you should not have 6
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
t+6=0 when t=?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
t=4
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
I already agreed with t=4 I don't agree with t=6 because 6+6 does not equal 0.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
t+6=0 when t=?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
right so the xintercepts of f(t)=16(t4)(t+6) are t=4 or t=6. Recall that anything that lays on the xaxis has the yvalue being 0. So the xintercepts in orderpair form are (4,0) or (6,0). Now what does t represent and what does y represent (or what does f(t) represent)? Refer to your problem for this. We are using this to interpret the xintercepts.
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
the height?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
which one is the height t or f(t)?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
the f and the t is time?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
right y=f(t) is the height t is the seconds Now I don't think we invented time travel yet and I think time travel would actually cause multiple dimensions (multiple possibilities) So I'm assuming time has to be 0 or greater that 0.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
So that means the one xintercept we found is not needed for this question. which one am I referring to?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
the (6,0)
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
you mean the (6,0)?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
yes
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
Yes (6,0)
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Ok so we only really have a graph for t>=0 or interval notation [0,infinity) So the only xintercept we have to determine is (4,0) since this point actually exists for t>=0.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so do you know what (4,0) means?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
I will give you a hint. You already said t represented seconds And f(t) or y whichever one you want to call it represents height
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so use this to say in words what (4,0) means
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
its the x intercept
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
It is 4 feet heigh at 0 secs
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
why do you say that? do you think the point should be read (4,0) or (0,4) you are getting confused which is which
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
we should really say tintercept when we say xintercept since there is no x's lol but anyways isn't it (t,y) not (y,t)?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
you said earlier t=4 now you are saying t=0
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
lol true. Yes t was first
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
So at 4 secs it was at 0 feet high
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
So we are definitely not interpreting (0,4) I'm not even sure this point is on the graph unless I check it but that is unnecessary work. We are looking at (4,0). which says yes after 4 seconds, the sandbag is 0 ft from the ground (or on the ground).
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
because you know if it has 0 distance from the ground then it is got to be on the ground right?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
right
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
ok Do you feel like you understand this problem better? Do you feel like if your teacher asked you to explain you would have the confidence to do so?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Do you have any questions?
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
I think so. But I am def looking into a tutor. lol
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
You might want to try to work this problem without looking at what we did from the very beginning and see if you arrive at the same conclusions as we did.
 one month ago

Cheyenne10.22 Group TitleBest ResponseYou've already chosen the best response.1
No questions. Thats a good idea. Thank you so very much for your help
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
np You deserve a medal for putting in work and not giving up on the problem. I see so many people give up. It really is awesome to come across people like you who care to understand it. Thanks for trying super hard.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Now I must return to my work. Good luck.
 one month ago
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