7
AssignmentMultiple Choice

The Quadratic Formula

Question 7 • Fall 24 GMS Advanced Algebra: Concepts and Connections A

The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation h = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.

Answer
A
t 0.87 s
B
t 4 s
C
t = 8.5 s
D
t = 16 s

Explanation

At the canyon floor, the rock’s height is 0, so solve −16t² + 255 = 0. Using the quadratic formula gives t = ±√(255/16), which is approximately ±3.99 seconds. Since time after the rock is dropped must be positive, the rock reaches the floor in about 4 seconds, matching choice B, “t = 4 s.”

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