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A dolphin is jumping out of the water. The function f(t)=-15t²+20t models the height in feet after t seconds of the dolphin. What do the coordinates of both x-intercepts represent in context of the dolphin? The x-intercepts coordinates represent the highest height and time it took for the dolphin to jump up and back down. The coordinates of the x-intercepts are the starting time/height and ending time/height of the dolphin's jump. O The coordinates of the x-intercepts are the axis of symmetry of the dolphin's path

A dolphin is jumping out of the water. The function f(t)=-15t²+20t models the height in feet after t seconds of the dolphin. What do the coordinates of both x-intercepts represent in context of the dolphin? The x-intercepts coordinates represent the highest height and time it took for the dolphin to jump up and back down. The coordinates of the x-intercepts are the starting time/height and ending time/height of the dolphin's jump. O The coordinates of the x-intercepts are the axis of symmetry of the dolphin's path

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section4.3: Writing Equations Of Parallel And Perpendicular Lines
Problem 16Q
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### Understanding the Path of a Dolphin’s Jump **Scenario Overview:** A dolphin is shown jumping out of the water in the image provided. This section explains how we can use a quadratic function to model the height of the dolphin during its jump. **Mathematical Model:** The function \( f(t) = -15t^2 + 20t \) represents the height in feet of the dolphin after \( t \) seconds. We want to understand what the coordinates of the x-intercepts signify within this context. **Question:** What do the coordinates of both x-intercepts represent in context of the dolphin’s jump? 1. The x-intercepts coordinates represent the highest height and time it took for the dolphin to jump up and back down. 2. The coordinates of the x-intercepts are the starting time/height and ending time/height of the dolphin's jump. 3. The coordinates of the x-intercepts are the axis of symmetry of the dolphin's path. **Correct Answer:** The coordinates of the x-intercepts are the starting time/height and ending time/height of the dolphin's jump. **Explanation:** - The x-intercepts of the function \( f(t) = -15t^2 + 20t \) are the points where the height of the dolphin is zero, meaning the dolphin is at the surface of the water. - The x-coordinate of these intercepts indicates the times when the dolphin starts and finishes the jump (when \( t = 0 \) and when \( t \) is the other x-intercept). **Graphical Representation:** Although no specific graph is provided in the image, let's break down the function graphically: 1. The quadratic equation will form a parabolic shape opening downwards, as indicated by the negative coefficient of \( t^2 \) (-15). 2. The vertex of the parabola represents the highest point of the dolphin’s jump. 3. The x-intercepts will be the points where the parabola crosses the t-axis (indicating the times when the height is zero). By analyzing the function and its intercepts, we can gain a clear understanding of the dolphin's jump duration and initial and final positions.
Transcribed Image Text:### Understanding the Path of a Dolphin’s Jump **Scenario Overview:** A dolphin is shown jumping out of the water in the image provided. This section explains how we can use a quadratic function to model the height of the dolphin during its jump. **Mathematical Model:** The function \( f(t) = -15t^2 + 20t \) represents the height in feet of the dolphin after \( t \) seconds. We want to understand what the coordinates of the x-intercepts signify within this context. **Question:** What do the coordinates of both x-intercepts represent in context of the dolphin’s jump? 1. The x-intercepts coordinates represent the highest height and time it took for the dolphin to jump up and back down. 2. The coordinates of the x-intercepts are the starting time/height and ending time/height of the dolphin's jump. 3. The coordinates of the x-intercepts are the axis of symmetry of the dolphin's path. **Correct Answer:** The coordinates of the x-intercepts are the starting time/height and ending time/height of the dolphin's jump. **Explanation:** - The x-intercepts of the function \( f(t) = -15t^2 + 20t \) are the points where the height of the dolphin is zero, meaning the dolphin is at the surface of the water. - The x-coordinate of these intercepts indicates the times when the dolphin starts and finishes the jump (when \( t = 0 \) and when \( t \) is the other x-intercept). **Graphical Representation:** Although no specific graph is provided in the image, let's break down the function graphically: 1. The quadratic equation will form a parabolic shape opening downwards, as indicated by the negative coefficient of \( t^2 \) (-15). 2. The vertex of the parabola represents the highest point of the dolphin’s jump. 3. The x-intercepts will be the points where the parabola crosses the t-axis (indicating the times when the height is zero). By analyzing the function and its intercepts, we can gain a clear understanding of the dolphin's jump duration and initial and final positions.
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