Select The Correct Answer.Dan Uses A Remote Control To Make His Drone Take Off From The Ground. The Function $h(t) = -16(t-2)^2 + 64$ Represents The Height, In Feet, Of The Drone $t$ Seconds After It Begins Flying.Which Statement

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Introduction

In this article, we will explore the height function of a drone, represented by the equation h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64. This function describes the height of the drone in feet, tt seconds after it begins flying. We will analyze the given function and determine the correct statement regarding the drone's flight.

The Height Function

The height function of the drone is given by the equation h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64. This function represents a quadratic equation in the form of h(t)=a(t−h)2+kh(t) = a(t-h)^2 + k, where aa, hh, and kk are constants.

  • Vertex Form: The given function can be written in vertex form as h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64. In this form, the vertex of the parabola is at the point (h,k)=(2,64)(h, k) = (2, 64).
  • Axis of Symmetry: The axis of symmetry of the parabola is the vertical line passing through the vertex, which is x=h=2x = h = 2.
  • Direction of Opening: The parabola opens downward, as indicated by the negative coefficient of the squared term, −16-16.

Analyzing the Function

To understand the behavior of the drone's height, we need to analyze the function h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64.

  • Initial Height: At t=0t = 0, the height of the drone is h(0)=−16(0−2)2+64=64h(0) = -16(0-2)^2 + 64 = 64 feet.
  • Maximum Height: The maximum height of the drone occurs at the vertex of the parabola, which is at t=2t = 2 seconds. At this time, the height of the drone is h(2)=−16(2−2)2+64=64h(2) = -16(2-2)^2 + 64 = 64 feet.
  • Height at Time tt: For any time tt, the height of the drone is given by the function h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64. This function represents a downward-opening parabola with a vertex at (2,64)(2, 64).

Selecting the Correct Statement

Based on the analysis of the height function, we can determine the correct statement regarding the drone's flight.

  • Statement 1: The drone takes off from the ground at t=0t = 0 seconds and reaches a maximum height of 64 feet at t=2t = 2 seconds.
  • Statement 2: The drone's height is given by the function h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64, which represents a downward-opening parabola with a vertex at (2,64)(2, 64).
  • Statement 3: The drone's height is 64 feet at t=0t = 0 seconds and decreases to 0 feet at t=4t = 4 seconds.

Conclusion

In conclusion, the correct statement regarding the drone's flight is:

  • Statement 2: The drone's height is given by the function h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64, which represents a downward-opening parabola with a vertex at (2,64)(2, 64).

Introduction

In our previous article, we explored the height function of a drone, represented by the equation h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64. This function describes the height of the drone in feet, tt seconds after it begins flying. We analyzed the given function and determined the correct statement regarding the drone's flight.

Q&A Session

Here are some frequently asked questions about the height function of a drone:

Q: What is the initial height of the drone?

A: The initial height of the drone is 64 feet, which occurs at t=0t = 0 seconds.

Q: What is the maximum height of the drone?

A: The maximum height of the drone is 64 feet, which occurs at t=2t = 2 seconds.

Q: How does the height of the drone change over time?

A: The height of the drone decreases over time, as represented by the downward-opening parabola with a vertex at (2,64)(2, 64).

Q: What is the axis of symmetry of the parabola?

A: The axis of symmetry of the parabola is the vertical line passing through the vertex, which is x=h=2x = h = 2.

Q: What is the direction of opening of the parabola?

A: The parabola opens downward, as indicated by the negative coefficient of the squared term, −16-16.

Q: How can we determine the correct statement regarding the drone's flight?

A: We can determine the correct statement by analyzing the function h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64 and understanding the behavior of the drone's height.

Q: What is the correct statement regarding the drone's flight?

A: The correct statement is:

  • Statement 2: The drone's height is given by the function h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64, which represents a downward-opening parabola with a vertex at (2,64)(2, 64).

Conclusion

In conclusion, the height function of a drone is represented by the equation h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64. This function describes the height of the drone in feet, tt seconds after it begins flying. We analyzed the given function and determined the correct statement regarding the drone's flight.

Frequently Asked Questions

Here are some frequently asked questions about the height function of a drone:

Q: What is the height of the drone at t=4t = 4 seconds?

A: The height of the drone at t=4t = 4 seconds is h(4)=−16(4−2)2+64=0h(4) = -16(4-2)^2 + 64 = 0 feet.

Q: What is the height of the drone at t=1t = 1 second?

A: The height of the drone at t=1t = 1 second is h(1)=−16(1−2)2+64=64h(1) = -16(1-2)^2 + 64 = 64 feet.

Q: What is the axis of symmetry of the parabola?

A: The axis of symmetry of the parabola is the vertical line passing through the vertex, which is x=h=2x = h = 2.

Q: What is the direction of opening of the parabola?

A: The parabola opens downward, as indicated by the negative coefficient of the squared term, −16-16.

Conclusion

In conclusion, the height function of a drone is represented by the equation h(t)=−16(t−2)2+64h(t) = -16(t-2)^2 + 64. This function describes the height of the drone in feet, tt seconds after it begins flying. We analyzed the given function and determined the correct statement regarding the drone's flight.