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9. a) What does the function say the height of the ball was when it was 120cm from the y-axis? (Round your answer to the nearest tenth). b) What is the sign of this height? c) What is the position of the ball to the eraser tray? d) Write this ordered pairs and plot its point T on the graph.

9. a) What does the function say the height of the ball was when it was 120cm from the y-axis? (Round your answer to the nearest tenth). b) What is the sign of this height? c) What is the position of the ball to the eraser tray? d) Write this ordered pairs and plot its point T on the graph.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Mat115 Project Real mathematics is about medeling situations that eccur naturally, and using the model to understand what is happening, or maybe to predict what will happen in the future. The quadratic equation is often used in modeling. Quadratic functions and applications are a large part of the mathematics of the world around us. Any general problem involving areas is a quadratic problem. The force of gravity, which basically holds the universe as we know it together, can be modeled with a quadratic function. The standand form of a quadratic function is y= ax²+bx+c. In this project we are going to model the Ball Toss with a quadratic function. So at 30 cm intervals, we draw 4 vertical lines extending from the eraser tray to the top of the marker board. We number the lines with their distances from the left most vertical line (which serves as the y-axis).Each of our volunteers selects a line and stand facing it at close proximity to the board. Between the board and the volunteers, I toss the ball to the catcher. Each of the volunteers will mark the height above the eraser tray at which the ball crosses his/her line. We will measure and label the height from the eraser tray to the marks. We have the following data: M(0,23.5); N(30,37.2); P(60,35.8); Q(90,19.3) These data represent a set of ordered pairs or a function. Since this function has an infinite number of ordered pairs, we are going to find an equation that defines this function. So we should use an equation in x and y where x represents the first coordinate and y represents the second coordinate. We should create a coordinate plane by drawing a horizontal number line called the x-axis, and a vertical line called the y-axis. 1. In this specific model of ball toss a) What does the x-axis represent? b) What do the x-coordinates represent? C) What do the y-coordinates represent? 2. Display your data in the coordinate plane or plot the points using a graph paper (Consider each square 10cm).Make sure you label the axis and the points. 3. Draw a smooth curve containing these points. 4. What shape does the graph have? 5. How does this shape open? 6. What kind of function this graph represents? 7. Write the standard form of the equation that represents this function.
Transcribed Image Text:Mat115 Project Real mathematics is about medeling situations that eccur naturally, and using the model to understand what is happening, or maybe to predict what will happen in the future. The quadratic equation is often used in modeling. Quadratic functions and applications are a large part of the mathematics of the world around us. Any general problem involving areas is a quadratic problem. The force of gravity, which basically holds the universe as we know it together, can be modeled with a quadratic function. The standand form of a quadratic function is y= ax²+bx+c. In this project we are going to model the Ball Toss with a quadratic function. So at 30 cm intervals, we draw 4 vertical lines extending from the eraser tray to the top of the marker board. We number the lines with their distances from the left most vertical line (which serves as the y-axis).Each of our volunteers selects a line and stand facing it at close proximity to the board. Between the board and the volunteers, I toss the ball to the catcher. Each of the volunteers will mark the height above the eraser tray at which the ball crosses his/her line. We will measure and label the height from the eraser tray to the marks. We have the following data: M(0,23.5); N(30,37.2); P(60,35.8); Q(90,19.3) These data represent a set of ordered pairs or a function. Since this function has an infinite number of ordered pairs, we are going to find an equation that defines this function. So we should use an equation in x and y where x represents the first coordinate and y represents the second coordinate. We should create a coordinate plane by drawing a horizontal number line called the x-axis, and a vertical line called the y-axis. 1. In this specific model of ball toss a) What does the x-axis represent? b) What do the x-coordinates represent? C) What do the y-coordinates represent? 2. Display your data in the coordinate plane or plot the points using a graph paper (Consider each square 10cm).Make sure you label the axis and the points. 3. Draw a smooth curve containing these points. 4. What shape does the graph have? 5. How does this shape open? 6. What kind of function this graph represents? 7. Write the standard form of the equation that represents this function.
8. Use the 3 points M (0, 23.5); N (30, 37.2) and P (60, 35.8) that verify the equation you wrote in question #7 a) Find the quadratic polynomial that predicts y from x. (Hint: you should resolve a system of linear equation to find the coefficients of the equation). (Round your answers to the nearest ten thousandths). (Remember to show all your work) b) Is the leading coefficient positive or negative? c) Does your answer for question (8b) contradict with your answer for question (5)? (If yes, check your work over before you continue). 9. a) What does the function say the height of the ball was when it was 120cm from the y-axis? (Round your answer to the nearest tenth). b) What is the sign of this height? c) What is the position of the ball to the eraser tray? d) Write this ordered pairs and plot its point T on the graph. 10. a) At what values of x does the function say the ball should have hit the eraser tray? (Round the values of x to the nearest cm) b) Display these points I and J on the graph and write their coordinates. c) What are these points called? 11. a) At what distances from the y-axis was the ball 28 cm above the eraser tray? (Round your answers to the nearest cm) b) Write these ordered pairs and plot their points R and S on the graph. 12. a) At what distance from the y-axis was the ball at its highest point? (Round your answer to the nearest cm). b) What was the maximum height of the ball measured, of course, from the eraser tray? (Round your answer to the nearest cm). c) What is the name of this highest point of the graph? d) Write the coordinate of the highest point V and plot it on the graph.
Transcribed Image Text:8. Use the 3 points M (0, 23.5); N (30, 37.2) and P (60, 35.8) that verify the equation you wrote in question #7 a) Find the quadratic polynomial that predicts y from x. (Hint: you should resolve a system of linear equation to find the coefficients of the equation). (Round your answers to the nearest ten thousandths). (Remember to show all your work) b) Is the leading coefficient positive or negative? c) Does your answer for question (8b) contradict with your answer for question (5)? (If yes, check your work over before you continue). 9. a) What does the function say the height of the ball was when it was 120cm from the y-axis? (Round your answer to the nearest tenth). b) What is the sign of this height? c) What is the position of the ball to the eraser tray? d) Write this ordered pairs and plot its point T on the graph. 10. a) At what values of x does the function say the ball should have hit the eraser tray? (Round the values of x to the nearest cm) b) Display these points I and J on the graph and write their coordinates. c) What are these points called? 11. a) At what distances from the y-axis was the ball 28 cm above the eraser tray? (Round your answers to the nearest cm) b) Write these ordered pairs and plot their points R and S on the graph. 12. a) At what distance from the y-axis was the ball at its highest point? (Round your answer to the nearest cm). b) What was the maximum height of the ball measured, of course, from the eraser tray? (Round your answer to the nearest cm). c) What is the name of this highest point of the graph? d) Write the coordinate of the highest point V and plot it on the graph.
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