In this project we are going to model the Ball Toss with aquadratic function. So at 30 cm intervals, we draw 4 vertical linesextending from the eraser tray to the top of the marker board. Wenumber the lines with their distances from the left most verticalline (which serves as the y-axis).Each of our volunteers selects aline and stand facing it at close proximity to the board. Betweenthe board and the volunteers, I toss the ball to the catcher. Eachof the volunteers will mark the height above the eraser tray atwhich the ball crosses his/her line. We will measure and label theheight 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. Sincethis function has an infinite number of ordered pairs, we are goingto find an equation that defines this function. So we should use anequation in x and y where x represents the first coordinate and yrepresents the second coordinate. We should create a coordinateplane by drawing a horizontal number line called the x-axis, and avertical 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 orplot the points using a graph paper (Consider each   square 10cm).Make sure you label the axis and thepoints.

3. Draw a smooth curve containing thesepoints.

4. What shape does the graph have?

5. How does this shape open?

6. What kind of function this graphrepresents?

7. Write the standard form of the equation thatrepresents 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 thatpredicts y from x. (Hint: you should resolve a system of linearequation to find the coefficients of the equation). (Round youranswers to the nearest ten thousandths). (Remember to show all yourwork)

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 yourwork over before you continue).

9. a) What does the function say the height ofthe ball was when it was 120cm from the y-axis? (Round your answerto the nearest tenth).

   b) What is the sign of this height?

   c) What is the position of the ball to the erasertray?

   d) Write this ordered pairs and plot its point T onthe graph.

10. a) At what values of x does the functionsay the ball should have hit the eraser tray? (Round the values ofx to the nearest cm)

      b) Display these points I and Jon the graph and write their coordinates.

      c) What are these pointscalled?

11. a) At what distances from the y-axis wasthe ball 28 cm above the eraser tray?(Round your answers to thenearest cm)

     b) Write these ordered pairs and plottheir points R and S on the graph.

12. a) At what distance from the y-axis was theball at its highest point?(Round your answer to the nearestcm).

     b) What was the maximum height of theball measured, of course, from the eraser tray? (Round your answerto the nearest cm).

     c) What is the name of this highestpoint of the graph?

     d) Write the coordinate of the highestpoint V and plot it on the graph.

please answer q2, q3,24,q5,q6 and q11,q12