Mat115 Project Real mathematics is about medeling situations that eccur naturally, and using the model to understand what is happening, er maybe to predict what will happen in the future. The quadratic equation is often used in medeling. 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. Ihe 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 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.

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