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.
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)?
@welshfella

- anonymous

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- welshfella

first simplify the function by taking out -16
so
y = -16(t^2 + 2t - 24 )

- welshfella

can you factor the quadratic in the parentheses?

- anonymous

yes hang on one sec please

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## More answers

- anonymous

f(t)=−16(t+6)(t−4)

- anonymous

So thats it for part A?

- anonymous

wait what would be the meaning???

- welshfella

right
now f(t) = the height of the sandbag at t seconds so it you put f(t) = 0
what do the values of t signify?

- anonymous

t is seconds?

- welshfella

- there will be 2 x-intercepts

- welshfella

t is seconds yes

- anonymous

wait im lost sorry

- anonymous

ok so Part A would be f(t)=−16(t+6)(t−4) where t is equaled to seconds?

- welshfella

f(t) = -16(t + 6)( t - 4) = 0
find values of t

- welshfella

- the x intercepts are values of t when f(t) the height = 0.

- anonymous

So the x-intercepts or t are equaled to -6 and 4?

- welshfella

right - now you neglect -6 The value t = 4 means the time when height of the sandbag from the ground = 0. That is when it lands.

- anonymous

So Part A is the factored function: f(t)=−16(t+6)(t−4) where the x-intercepts or t represents the time in seconds that the sandbag was thrown?

- anonymous

and the x-intercept is (4,0) which represents the time in seconds that the sandbag was thrown?

- anonymous

to where it lands

- anonymous

@welshfella

- anonymous

for Part b the completing of the square is: (t+1)^2=25 right

- welshfella

yes t = 0 is the time when in is thrown and t = 4 = when it lands

- welshfella

don't forget the -16

- anonymous

ok so part a is complete!

- anonymous

Wait the -16 for what??

- anonymous

@welshfella

- welshfella

part a is complete yes
the function is -16(t^2 + 2t - 24)

- anonymous

the function is f(t)=−16(t+6)(t−4
For Part B: complete the square: (t+1)^2=25

- welshfella

-16(t^2 + 2t - 24)
= -16 [ (t + 1)^2 - 15]

- anonymous

now I have to find the vertex and decide whether it is a maximum or minimum

- welshfella

= -16 [ (t + 1)^2 - 25]

- welshfella

yes it will be a maximum because the coefficient of t^2 is negative

- anonymous

ok so (t+1)^2=25 is a maximum with the vertex or 400??

- anonymous

of^^^

- welshfella

excuse me i 'll be back in a minute or two...

- anonymous

ok

- welshfella

right the maximum point on the graph is when t+1 = 0 that s is t = -1
and f(t0 will equal 400
(-1,400)

- welshfella

the axis of symmetry is the vertical line passing through the point (-1,400) which is x = -1

- welshfella

* t = -1

- anonymous

ok I understand thanks so much! Is that everything??

- welshfella

oh they talk about f(x) in parts b and c which makes more sense than t as you cant have negative times! so - change all those references to t to x.

- anonymous

ok thank you! @welshfella I may need more help on other questions Ill tag you!!!!!!!!

- welshfella

ok yw

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