Question 555680: Help, please? I've been having trouble with these problems for my homework.
Use factoring to find the zeros of the quadratic function.
1) G(x)=x^2+5x
2) F(x)=x^2-x-6
3) f(x)=x^2+2x-120
An object is propelled vertically upward from the top of a 256-foot building. The quadratic function s(t)=-16t^2+176t+256 models the ball's height above the ground, s(t), in feet, t seconds after it was thrown. How many seconds does it take until the object finally hits the ground?
Any help really, I'd be tremendously grateful.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Use factoring to find the zeros of the quadratic function.
1) G(x)=x^2+5x
2) F(x)=x^2-x-6
3) f(x)=x^2+2x-120
An object is propelled vertically upward from the top of a 256-foot building. The quadratic function s(t)=-16t^2+176t+256 models the ball's height above the ground, s(t), in feet, t seconds after it was thrown. How many seconds does it take until the object finally hits the ground?
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1) G(x) = x^2 + 5x
Factor: x(x+5) = 0 -> x = 0, x = -5
2) F(x) = x^2 - x - 6
Factor: (x-3)(x+2) = 0 -> x = 3, x = -2
3) f(x) = x^2 + 2x - 120
Factor: (x-10)(x+12) = 0 -> x = 10, x = -12
At ground level s(t) = 0:
0 = s(t) = -16t^2 + 176t + 256
Dividing through by -16 gives t^2 - 11t - 16 = 0
Solve using the quadratic formula:
t = (11 +- sqrt(121 + 64))/2
This gives t = -1.3, 12.3
Obviously we need the positive solution, t = 12.3 s
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