Broskishelleh
  • Broskishelleh
A sandbag was thrown downward from a building. The function f(t) = -16t2 - 64t + 80 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)
Mathematics
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SOLVED
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katieb
  • katieb
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Broskishelleh
  • Broskishelleh
Please halp
Nnesha
  • Nnesha
given expression is f(t) where is f(x) or is it a typo ?
Broskishelleh
  • Broskishelleh
F(t) is F(x), just replace t with x if you want

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Nnesha
  • Nnesha
alright let's factor the right side i have few mints sorry
Broskishelleh
  • Broskishelleh
It's fine
Nnesha
  • Nnesha
\[\huge\rm f(t)= \color{ReD}{-16t^2-64t+80}\] first take out the common factor
Broskishelleh
  • Broskishelleh
The common factor is 8
Nnesha
  • Nnesha
well we need GREATEST common factor
Broskishelleh
  • Broskishelleh
Oh, 16 then my mistake
Nnesha
  • Nnesha
yes right and bec leading coefficient is negative we can take out the negative 16
Nnesha
  • Nnesha
and sorry gtg :(
Broskishelleh
  • Broskishelleh
Alright that leaves us with \[f(t) = -4 + 5\]
Broskishelleh
  • Broskishelleh
Okay bye
Nnesha
  • Nnesha
aw didn't get the help :( sorry
Nnesha
  • Nnesha
alright when we find the common denominator we should divide all terms by the common factor \[\large\rm \color{blue}{\frac{ -16t^2 }{ -16 }-\frac{ 64t }{ -16}+\frac{ 80 }{ -16} }\]\[\large \rm f(t)=-16(\color{blue}{t^2+4t-5})\] now factor t^2+4t-5 there are more than 3 ways to factor o the quadratic equation you can use AC method(easy) find two number when you multiply them you should get product of AC (a=leading coefficient , c=constant term) and when you add or subtract them you should get middle term(b)
Nnesha
  • Nnesha
remember t^2 is same as 1t^2 so in this question leading coefficient is 1

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