Real mathematics is about modeling situations that occur 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 standard 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 number intervals, we draw 4 vertical lines extending from the eraser tray to the top of the marker board. cm We our the lines with their distances from the left most vertical line (which serves as the y-axis).Each the volunteers selects a line and stand facing it at close proximity to the board. Between the board and of 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 ordered data represent a set of ordered pairs or a function. Since this function has an infinite number in x and y where x represents the first coordinate and y represents the second coordinate. We should pairs, we are going to find an equation that defines this function. So we should use an equation of the y-axis. create a coordinate plane by drawing a horizontal number line called the x-axis, and a vertical line called
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) (Remember equation Find to the find to quadratic show the coefficients all polynomial your work) of that the equation). predicts y (Round from X. your (Hint: answers you should to the resolve nearest a system ten of linear thousandths).
b) Is the leading coefficient positive or negative? work over before you continue).
c) Does your answer for question (8b) contradict with your answer for question (5)? (If yes, check your your answer to the nearest tenth). 9. a) What does the function say the height of the ball was when it was 120cm from the y-axis? (Round
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.

Real mathematics is about modeling situations that occur naturally,...