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 x-intercept of the function. (4 points)
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? (4 points)
Part C: Use your answer in part B to determine the axis of symmetry for f(x)? (2 points)
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well factor out -16 and you get
\[f(t) = -16(t^2 + 2t - 24)\]
now factor the quadratic
In part B it talks about f(x).... where does that come from... seeing the original equation is f(t)
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well you need to factor the quadratic in the brackets for A
find the factors of -24 that add to 2... the larger factor is positive...
that should be relatively easy
How do I find the factor of -24?
start with what are the factors of 24...
What can be multiplied to get 24?
Hello, @campbell_st ?
thats correct... what pairs multiply to 24
or you can work on what pairs multiply ti -24 and have a difference of 2
e.g. 24 and -1 difference = 23 12 and -2 difference = 10
Ok, so those are the factors of 24.
they are some of the factors of -24... but not the ones you need... what other pairs multiply to -24...?
-4 * 6
OHHHH and that has 2 number difference
great so the factored form is
\[f(t) = -16(t + 6)(t - 4)\]
so what do they mean.... here is a simply sketch
the only intercept you need to consider is 4.... and you are talking time... and we can't go back in time so ignore -6 as an intercept...
so what do you think t = 4 represents...?
forgot to say, to find the intercepts you need to solve the factors
t + 6 = 0 and t - 4 = 0
so t = -6 and t = 4?
or in actual fact the graph is probably more like
correct for the solutions.... there are the time values where then height is 0....
or the bag is on the ground...
since time can't be negative, you ignore the solution t = -6
does that make sense..?
So in the end t = 4?
But what im confused is, what do I write for "Part A: Factor the function f(t) and use the factors to interpret the meaning of the x-intercept of the function."
thats correct... and what it means is simply, that's when the bag hits the ground...
the so its a really poorly worded question, and you should raise it with your teacher...
they are talking about the horizontal axis... which is this case is used to show time (t)
-4 * 6 ( Factor of -24)
Answer = 4
Can I write that for A?
yes... and you are also asked what it means... t = 4 is the time it takes the bag to hit the ground.
Ok, so thats for A. Do you think you could help me with B?
well can you check the equation is -32t and not + 32t..?
The function f(t) = -16t2 - 32t + 384
nope its negative
Also, do you have skype campbell? may be easier
ok.... can you contact the instructor.... because the question makes no sense....
its because the maximum height for the object occurs when t = -1.....
which makes no sense... as that is 1 second before it is thrown from the window...
I'm about to go to school, but I'd be complaining to the teacher that this question makes absolutely no sense....
so here are the solutions you need
PArt B complete the square
\[f(t) = -16(t^2 + 2t + ?) + 384 \]
to complete the square add 1 inside the brackets whcih means adding 16 outside
\[f(t) = -16(t + 1)^2 + 400\]
the vertex is at (-1, 400)
Part C, the axis if symmetry is the t value in the vertex at t = -1
hope it helps