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anonymous
 one year ago
A sandbag was thrown downward from a building. The function f(t) = 16t2  32t + 384 shows the height f(t), in feet, of the sandbag after t seconds:
Part A: Factor the function f(t) and use the factors to interpret the meaning of the xintercept of the function.
Part B: Complete the square of the expression for f(x) to determine the vertex of the graph of f(x). Would this be a maximum or minimum on the graph?
Part C: Use your answer in part B to determine the axis of symmetry for f(x)?
anonymous
 one year ago
A sandbag was thrown downward from a building. The function f(t) = 16t2  32t + 384 shows the height f(t), in feet, of the sandbag after t seconds: Part A: Factor the function f(t) and use the factors to interpret the meaning of the xintercept of the function. Part B: Complete the square of the expression for f(x) to determine the vertex of the graph of f(x). Would this be a maximum or minimum on the graph? Part C: Use your answer in part B to determine the axis of symmetry for f(x)?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for part A i got 16(t+6)(x4) when factored and said that the xintercepts of the functions is (4,0) which represents the time in seconds that the sandbag was thrown to where it lands.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For part b I completed the square and got (t+1)^2 = 25 but how do I find the vertex?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Hero @Hero you said you would help me!

Hero
 one year ago
Best ResponseYou've already chosen the best response.0I said, post your next question separately. Anyone can help with these.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah I did post it separately and you said you would help!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need help on finding the vertex and I am confused on how to

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3For Part A, you are correct (almost)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What did I leave out? @TheSmartOne could you please explain

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3It's a simply mistake, but: You were given \(\sf\Large f(t) = 16t^2  32t + 384\) however you factored it to \(\sf\large 16(t+6)(\color{red}{x}4)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the t in t4 is supposed to be x4? @TheSmartOne

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3The variable you were given @kaite_mcgowan was \(\bf t\) so I don't understand where you brought in the \(\bf x\) from. So you just need to change the x to a t to make it correct :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok thanks so much! could you please help me on b and finding the vertex with the completed square of (t+1)^2 = 25 @TheSmartOne

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3\(\sf\Large y=a(xh)^2+k\) The vertex is \(\sf\Large (h,k)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so how would I incorporate (t+1)^2 = 25 in to that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y = a(t1)^2 + 25 ???? @TheSmartOne

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3You didn't properly complete the square.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0?? what do you mean?

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3\(\sf\Large 16t^2  32t + 384 \color{red}{\neq} (t1)^2+25\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the completed square form is (t  1)^2 + 25

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3it isn't. That's wrong.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok i got it. How would I find it then?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0could you show me step by step

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3\(\sf\Large 16t^2  32t =384\) What is \(\sf\Large\left( \frac{b}{2}\right)^2=\left( \frac{32}{2}\right)^2=?\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0whats next ??? @TheSmartOne

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3you have to add it to both sides: \(\sf\Large 16t^2  32t+(16^2) =384+(16)^2\)

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3can you factor the left hand side? Hint: \(\sf\Large a^2+2ab+b^2=(a+b)^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am so sorry i lost wifi! @TheSmartOne

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so you get 16t^2  32t + (256) = 384 + (256) @TheSmartOne

anonymous
 one year ago
Best ResponseYou've already chosen the best response.016t^2  32t + (256) = 640 @TheSmartOne

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3One sec, we'll need to backtrack over here

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you know what went wrong?

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3we have to first factor the 16 out of the equation, so: \(\sf\Large 16t^2  32t + 384 =16(t^2+2t24) \)

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3@Mehek14 @paki I'm not sure how to complete the square :/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the factored form is 16(t+6)(t4)

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3there are so many ways to solve math, I don't know why they limit us with this completing the square lol

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3https://mathway.com/examples/Algebra/QuadraticEquations/SolvebyCompletingtheSquare?id=29 mhmmm

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait thats the answer the link above? I know that the highest point or the maximum is 400 and the symmetry of axis is 1???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i just dont understand completing the square?

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3the link was an example of how to do it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok so what would I do ??

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3yes, the symmetry of axis is x=1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok I go that part and I know that the maximum is 400 i just need to show my work of how I got that

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3@zepdrix could you help us to complete the square for \(\sf\Large f(t)=16t^232t+384\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@zepdrix please I really need help!

Mehek14
 one year ago
Best ResponseYou've already chosen the best response.0I can tell you how to do the first step

Mehek14
 one year ago
Best ResponseYou've already chosen the best response.0divide all the numbers by 16

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3the calculator gives you the final answer, but no steps: http://prntscr.com/7metrk

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3@mathmate could you help us complete the square?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OMG EVERYONE I THINK I MAY HAVE FIGURED IT OUT! GIVE ME ONE SEC!

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3we could have just as easily found the vertex by b/2a ¯\_(ツ)_/¯

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a(x+d)2+e d=−32 / 2⋅(−16) d=1 e=384− (−32)^2 / 4⋅(−16) e=400 −16(t+1)2+400

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0that's it, I've been working it out over here as well. nicely done. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks so much!!!! @jtvatsim

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3well we got the completing square out of the way

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3\(\color{blue}{\text{Originally Posted by}}\) @TheSmartOne \(\sf\Large y=a(xh)^2+k\) The vertex is \(\sf\Large (h,k)\) \(\color{blue}{\text{End of Quote}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0haha yep! so to find the vertex I wold just do y = 16(x1)^2 +400??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or in other words the vertex is (1,400)

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3and that would be a maximum or a minimum?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for all of your help @TheSmartOne and sticking with me through the whole equation unlike other people who promised before **cough cough @Hero cough cough** thanks again @TheSmartOne

Hero
 one year ago
Best ResponseYou've already chosen the best response.0I had to go to lunch. I would have helped otherwise.

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.3I probably wouldn't have helped if it wasn't for Hero: http://prntscr.com/7mezsj

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0at least hero considered it...

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0@kaite_mcgowan Is the question resolved?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes it is thanks for asking! @mathmate

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I came a little late. Here's what I would have done anyway: Given f(t)=\(16t^232t+384\) (a) factorization f(t)=\(16(t^2+2t24)\) f(t)=16(t+6)(t4) (b) Complete square f(t)=16(t+1 +5)(t+1 5) f(t)=16[(t+1)^225] maximum is at x=1 (solve for t in t+1=0), f(1)=400. Maximum because leading coefficient (of t^2) is negative. (c) Axis of symmetry Axis of symmetry of a quadratic is location of maximum/minimum, i.e. x=1
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