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 9 months ago
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
 9 months ago
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

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myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4Are you having trouble factoring?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4f(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.

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1I 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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4Part A: Says to factor to get the xintercepts. Did you factor yet?

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1I think I did it wrong thats where I got a( (8, 320)

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4(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

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1Ok so how factor the function?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4I 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.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4Can you identify a,b, and c?

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1a would be 16, b would be 32, and 384 is c, right?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4I think you had some negative numbers. I know they aren't all positive.

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1sorry 16 and 32 were negative

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4so 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.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4You could try to make life easier and see if 16, 32,384 have a common factor (greater than one)?

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1ok Im trying to find that now. Ok hold on

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4Though you could do this with the bigger numbers.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4cool so lets see what happens when we factor 16 out from 16t^232t+384

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4\[16(\frac{16t^2}{16}\frac{32t}{16}+\frac{384}{16})\]

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4so 16/16=? and 32/16=? and 384/16=?

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.116/16=1 32/16=2 384/16=24

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4so 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 \[t^2+2t24\]

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4We aren't done factoring.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4I'm asking you to reidentify a,b,and c.

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1oh ok sorry. as you may can tell math isnt my best subject

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4we need to find a*c after. Then we need to find two factors of a*c that have product ac and sum b.

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1a= t^2 b= 2t c= 24 right

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4a,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)

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4we 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

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1Im so confused. wouldn't the factor be 16(t+1624)

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4Where did you get 16(t+1624) I thought we had 16(t^2+2t24)

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1I'm not sure. was trying to factor I think I just put the wrong number in.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4ok 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.

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1a=1t^2 b=2t c=24

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4again 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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4a=1 b=2 c=24 now what is a*c

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4ok 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?

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1i thought that was a 7. Im lost again

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4which 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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4can you tell what we were looking for?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4i actually told you what we were looking for.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4and where are you lost? I haven't see any 7's yet

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1it was the ? no 7 We were getting the b and c right

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4My 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?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4so 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)

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4You may want to work on more factoring.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4So what are the xintercepts?

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1Yes I do. the 6 and 4 right

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1yes I do. the 6 and 4 right

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.44 is right but you should not have 6

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4I already agreed with t=4 I don't agree with t=6 because 6+6 does not equal 0.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4right 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.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4which one is the height t or f(t)?

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1the f and the t is time?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4right 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.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4So that means the one xintercept we found is not needed for this question. which one am I referring to?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4you mean the (6,0)?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4Ok 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.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4so do you know what (4,0) means?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4I 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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4so use this to say in words what (4,0) means

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1its the x intercept

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1It is 4 feet heigh at 0 secs

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4we 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)?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4you said earlier t=4 now you are saying t=0

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1lol true. Yes t was first

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1So at 4 secs it was at 0 feet high

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4So 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).

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4because you know if it has 0 distance from the ground then it is got to be on the ground right?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4ok 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?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4Do you have any questions?

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1I think so. But I am def looking into a tutor. lol

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4You 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.

Cheyenne10.22
 9 months ago
Best ResponseYou've already chosen the best response.1No questions. Thats a good idea. Thank you so very much for your help

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4np 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.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.4Now I must return to my work. Good luck.
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