 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that graph y is equal to 4x cube plus 32x square minus 9x minus 72 using appropriate window on graphing calculator. Now let us start with the solution of the given question. We are given a polynomial function y is equal to 4x cube plus 32x square minus 9x minus 72. We will graph it using suitable window. Now this is the TI-83 plus calculator and we want to graph this polynomial function on it. First we begin with home screen and press y is equal to button. This takes us to the equation entering screen where we will write our equation. Now let us enter equation into y1. Here we write the equation 4x cube plus 32x square minus 9x minus 72 using xt theta n key. After writing this equation, we will get this screen. To view its graph, we press graph key. On the screen, the graph of the polynomial function y is equal to 4x cube plus 32x square minus 9x minus 72 will appear on the coordinate axis. Now this is 10 by 10 viewing window. It means the x axis is from minus 10 to 10 and y axis is also from minus 10 to 10 and this is the standard window but it is not giving proper view of the graph. Now to have better view of the graph, we can adjust this window. To adjust window screen, we press window key and this screen will be displayed. Let us discuss the window settings and their meanings. Now xmin and xmax are the leftmost and rightmost values to use on the x axis. Similarly, ymin and ymax are the smallest and largest values to use on the y axis. Yscl and xscl are the units or scale to use on the y axis and x axis respectively. If yscl is equal to 1, then each interval on the y axis is 1 unit and if xscl is equal to 1, then each interval on the x axis is 1 unit. When writing our window information on paper, we indicate the viewing window by stating closed interval from xmin to xmax by closed interval from ymin to ymax that is using closed intervals such as closed interval from minus 10 to 10 by closed interval from minus 10 to 10. So here, let us choose the window that is closed interval from minus 9 to 3 by closed interval from minus 100 to 300. So here we change xmin value to minus 9 and we should note that the minus sign here is not the subtraction sign. We press negative sign given by this key otherwise we will get error. Then we scroll down and change xmax value to 3. Similarly, we write ymin as minus 100 and ymax as 300. Let us keep the scale on x axis as it is of 1 unit but since y axis is taken as closed interval from minus 100 to 300 which is quite large so we choose scale of 50 on y axis. Now we press graph key. We get this display of the graph on the screen. Now this window is better than 10 by 10 window display. Now using this window we are getting a clear idea of the graph thus choosing appropriate window gives better display of graph. Now we press trace key to know the value of the coordinates and we get this display on the screen. Here we see that this point on the graph shows when x is equal to minus 3 y is equal to 135 and this is the required appropriate display. This completes our session. Hope you enjoyed this session.