The height above ground (in feet) of a ball thrown vertically into the air is given by the equation:\[ S = 80t - 16t^2 \]where $ t $ is the time in seconds since the ball was thrown.### (a) Graph this equation with a graphing calculator- **Graph 1** - The x-axis (horizontal) represents time $ t $, ranging from -2 to 10. - The y-axis (vertical) represents the height $ S $, ranging from 0 to 150. - The graph is a downward-opening parabola that represents the height of the ball over time. - The parabola peaks at its vertex, indicating the maximum height of the ball.- **Graph 2** - The x-axis represents time $ t $, ranging from -10 to 2. - The y-axis represents the height $ S $, ranging from -150 to 20. - The graph shows a partial parabola with most of it being below the x-axis.- **Graph 3** - The x-axis represents time $ t $, ranging from -2 to 10. - The y-axis represents the height $ S $, ranging from -150 to 0. - The graph shows a partial parabola that primarily lies below the x-axis.**Correct Graph:** The first graph is the correct representation for this situation, with the ball being at its highest point above the ground.### (b) Estimate the time at which the ball is at its highest point, and estimate the height of the ball at that time.- **Estimated Time $ t $:** 2 seconds- **Estimated Height $ S $:** 80 feetThese estimates are typically verified by finding the vertex of the parabola, which can be calculated using the formula $ t = -\frac{b}{2a} $ for the equation $ S = at^2 + bt + c $, where here $ a = -16 $, $ b = 80 $, and $ c = 0 $. The vertex gives the time at the highest point, and substituting back gives the height.

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The height above ground (in feet) of a ball thrown vertically into the air is given by S- Bot - 16t2 where t is the time in seconds since the ball was thrown. (a) Graph this equation with a graphing calculator and the window t-min = -2, t-max = 10; S-min = -20, S-max = 150. S 150 150 -10 -8 -6 -4 -2 2 -2 4 6 8 10 100 100 -50 50 -100 -100 -2 4 6. 10 -10 -8 -6 -4 -2 -150 -150 (b) Estimate the time at which the ball is at its highest point, and estimate the height of the ball at that time. t 16 S- 90

The height above ground (in feet) of a ball thrown vertically into the air is given by S- Bot - 16t2 where t is the time in seconds since the ball was thrown. (a) Graph this equation with a graphing calculator and the window t-min = -2, t-max = 10; S-min = -20, S-max = 150. S 150 150 -10 -8 -6 -4 -2 2 -2 4 6 8 10 100 100 -50 50 -100 -100 -2 4 6. 10 -10 -8 -6 -4 -2 -150 -150 (b) Estimate the time at which the ball is at its highest point, and estimate the height of the ball at that time. t 16 S- 90

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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The height above ground (in feet) of a ball thrown vertically into the air is given by the equation:

\[ S = 80t - 16t^2 \]

where $ t $ is the time in seconds since the ball was thrown.

### (a) Graph this equation with a graphing calculator

- **Graph 1**
- The x-axis (horizontal) represents time $ t $, ranging from -2 to 10.
- The y-axis (vertical) represents the height $ S $, ranging from 0 to 150.
- The graph is a downward-opening parabola that represents the height of the ball over time.
- The parabola peaks at its vertex, indicating the maximum height of the ball.

- **Graph 2**
- The x-axis represents time $ t $, ranging from -10 to 2.
- The y-axis represents the height $ S $, ranging from -150 to 20.
- The graph shows a partial parabola with most of it being below the x-axis.

- **Graph 3**
- The x-axis represents time $ t $, ranging from -2 to 10.
- The y-axis represents the height $ S $, ranging from -150 to 0.
- The graph shows a partial parabola that primarily lies below the x-axis.

**Correct Graph:** The first graph is the correct representation for this situation, with the ball being at its highest point above the ground.

### (b) Estimate the time at which the ball is at its highest point, and estimate the height of the ball at that time.

- **Estimated Time $ t $:** 2 seconds
- **Estimated Height $ S $:** 80 feet

These estimates are typically verified by finding the vertex of the parabola, which can be calculated using the formula $ t = -\frac{b}{2a} $ for the equation $ S = at^2 + bt + c $, where here $ a = -16 $, $ b = 80 $, and $ c = 0 $. The vertex gives the time at the highest point, and substituting back gives the height.

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