anonymous
  • anonymous
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
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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welshfella
  • welshfella
first simplify the function by taking out -16 so y = -16(t^2 + 2t - 24 )
welshfella
  • welshfella
can you factor the quadratic in the parentheses?
anonymous
  • anonymous
yes hang on one sec please

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anonymous
  • anonymous
f(t)=−16(t+6)(t−4)
anonymous
  • anonymous
So thats it for part A?
anonymous
  • anonymous
wait what would be the meaning???
welshfella
  • 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
  • anonymous
t is seconds?
welshfella
  • welshfella
- there will be 2 x-intercepts
welshfella
  • welshfella
t is seconds yes
anonymous
  • anonymous
wait im lost sorry
anonymous
  • anonymous
ok so Part A would be f(t)=−16(t+6)(t−4) where t is equaled to seconds?
welshfella
  • welshfella
f(t) = -16(t + 6)( t - 4) = 0 find values of t
welshfella
  • welshfella
- the x intercepts are values of t when f(t) the height = 0.
anonymous
  • anonymous
So the x-intercepts or t are equaled to -6 and 4?
welshfella
  • 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
  • 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
  • anonymous
and the x-intercept is (4,0) which represents the time in seconds that the sandbag was thrown?
anonymous
  • anonymous
to where it lands
anonymous
  • anonymous
@welshfella
anonymous
  • anonymous
for Part b the completing of the square is: (t+1)^2=25 right
welshfella
  • welshfella
yes t = 0 is the time when in is thrown and t = 4 = when it lands
welshfella
  • welshfella
don't forget the -16
anonymous
  • anonymous
ok so part a is complete!
anonymous
  • anonymous
Wait the -16 for what??
anonymous
  • anonymous
@welshfella
welshfella
  • welshfella
part a is complete yes the function is -16(t^2 + 2t - 24)
anonymous
  • anonymous
the function is f(t)=−16(t+6)(t−4 For Part B: complete the square: (t+1)^2=25
welshfella
  • welshfella
-16(t^2 + 2t - 24) = -16 [ (t + 1)^2 - 15]
anonymous
  • anonymous
now I have to find the vertex and decide whether it is a maximum or minimum
welshfella
  • welshfella
= -16 [ (t + 1)^2 - 25]
welshfella
  • welshfella
yes it will be a maximum because the coefficient of t^2 is negative
anonymous
  • anonymous
ok so (t+1)^2=25 is a maximum with the vertex or 400??
anonymous
  • anonymous
of^^^
welshfella
  • welshfella
excuse me i 'll be back in a minute or two...
anonymous
  • anonymous
ok
welshfella
  • 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
  • welshfella
the axis of symmetry is the vertical line passing through the point (-1,400) which is x = -1
welshfella
  • welshfella
* t = -1
anonymous
  • anonymous
ok I understand thanks so much! Is that everything??
welshfella
  • 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
  • anonymous
ok thank you! @welshfella I may need more help on other questions Ill tag you!!!!!!!!
welshfella
  • welshfella
ok yw

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