Solving Quadratic Word Problems

8. The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

• 3 seconds

• 2 seconds

• 4 seconds

• 6 seconds

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

• 5 seconds

• 1 second

• 2 seconds

• 3 seconds

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t² + 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

*Hint: For this problem, the concept is the same, but the factoring method has changed to GCF only.

• 0.5 seconds

• 1 second

• 1.5 seconds

• 2 seconds

• 3 seconds

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds. When is the ball at ground level? *Hint: For this problem, the concept is the same, but the factoring method for this one has changed to GCF and Difference of Squares.

• only at t = 0 seconds

• only at t = 3 seconds

• only at t = 9 seconds

• at both t = 0 seconds and t = 3 seconds

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The height of the ball t seconds after it is thrown is given by the formula h(t) = -10t² +40.

How many seconds after the ball is thrown will it return to the ground?

*No hint this time.

• 2 seconds

• 4 seconds

• 6 seconds

• 8 seconds

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

• 2.625

• 6.25

• 100

• 200

• 210.25

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation s(t) = –16t² + 64t + 80. What will be the object's maximum height? 

• 2 ft

• 80 ft

• 144 ft

• 64 ft

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t  
When will the object reach its maximum height?

• 4 ft

• 0 seconds

• 0 ft

• 4 seconds

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function
 h = -16t² + 64t + 960.
How many seconds did it take for the ball to reach its maximum height?

• 10 seconds

• 64 seconds

• 960 seconds

• 2 seconds

Your cousin hit a golf ball with an initial velocity of 27 feet per second. The equation h = -6t² + 27t models the golf ball's height in feet t seconds after the ball was hit. How long after being hit did the ball reach maximum height?

• 1 second

• 2.25 seconds

• 3 seconds

• 4.5 seconds

• 5 seconds