Distance calculation of two points by using parametric equations for teaching and learning processes

Time and distance data were collected to obtain a polynomial graph by plotting the distances of x and y versus time, t and to determine a parametric equation form for two of the quadratic equations. To begin the experiment, data on time in minutes from the initial point, Subang Jaya to the end point, Taman Melati was collected and marked in Table 1. The first data of time, t was added to the second one to achieve the second data of time, t for all 27 data of time, t. The distances of x and y were likewise measured and recorded. This process was repeated for 26 times to achieve additional sets of results. From the plotting of x versus t and y versus t, two polynomial graphs were obtained. From here, two quadratic equations were obtained with the highest power of 2. Since one of the equations has a negative determinant value, which is the x(t) equation, this implies a maximum value graph whereas the y(t) equation has a positive determinant value, which infers a minimum value graph of a polynomial. Moreover, an elimination method was conducted on both the x(t) and y(t) equations. When the equation of x(t) was rewritten in the form ax2 +bx+c=0, t in terms of x equation was obtained. From there, t(x) was inserted into y(t) to achieve a y(x) equation.