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5. A ball is thrown upward from the top of a building. The Batt height above ground can be modeled by the equaron H(t) = -12t2 + 60t+40. Whến will the ball reach thee maximum height? What he maximum height.of-the bal?

5. A ball is thrown upward from the top of a building. The Batt height above ground can be modeled by the equaron H(t) = -12t2 + 60t+40. Whến will the ball reach thee maximum height? What he maximum height.of-the bal?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please help. If you can please explain why each step is done . It helps me a lot . Thank you! 

Certainly! Here's a transcription of the text for an educational website: --- ### Problem Statement **5.** A ball is thrown upward from the top of a building. The height above ground can be modeled by the equation \( h(t) = -16t^2 + 4t + 90 \), where \( h \) is the height in feet and \( t \) is the time in seconds after the ball is thrown. **Question:** What maximum height does the ball reach? --- ### Annotations and Notes - **Input Function**: The equation \( h(t) = -16t^2 + 4t + 90 \) is identified as the input function. - **Parabola Vertex**: The vertex of the parabola represents the maximum height of the ball. - **The Vertex**: Indicates the maximum point on the graph. - **The Max**: Refers to the maximum height, which is the vertex of the parabola. - **At t = ?**: Specifies the point in time at which the maximum height is achieved. --- ### Explanation The problem involves a quadratic equation modeling the motion of a ball thrown upwards. The height function \( h(t) = -16t^2 + 4t + 90 \) describes a parabola opening downwards, indicating that the highest point is at the vertex. To find the maximum height, determine the vertex of the parabola using the formula for the time at which the vertex occurs, \( t = -\frac{b}{2a} \), for the quadratic equation \( ax^2 + bx + c \).
Transcribed Image Text:Certainly! Here's a transcription of the text for an educational website: --- ### Problem Statement **5.** A ball is thrown upward from the top of a building. The height above ground can be modeled by the equation \( h(t) = -16t^2 + 4t + 90 \), where \( h \) is the height in feet and \( t \) is the time in seconds after the ball is thrown. **Question:** What maximum height does the ball reach? --- ### Annotations and Notes - **Input Function**: The equation \( h(t) = -16t^2 + 4t + 90 \) is identified as the input function. - **Parabola Vertex**: The vertex of the parabola represents the maximum height of the ball. - **The Vertex**: Indicates the maximum point on the graph. - **The Max**: Refers to the maximum height, which is the vertex of the parabola. - **At t = ?**: Specifies the point in time at which the maximum height is achieved. --- ### Explanation The problem involves a quadratic equation modeling the motion of a ball thrown upwards. The height function \( h(t) = -16t^2 + 4t + 90 \) describes a parabola opening downwards, indicating that the highest point is at the vertex. To find the maximum height, determine the vertex of the parabola using the formula for the time at which the vertex occurs, \( t = -\frac{b}{2a} \), for the quadratic equation \( ax^2 + bx + c \).
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