 Hello and welcome to the session. In this session we will discuss how to graph polynomial functions on graphing that is TI-83 plus calculator using an appropriate window and we will also learn how to find its root on the graph. Let us consider the polynomial function. y is equal to x cube minus 5x square minus x plus 5. Now we will graph it using suitable window. This is the TI-83 plus calculator and we want to graph the 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. We write x cube minus 5x square minus x plus 5 using x t theta n key. After writing the equation we will get this screen. To view its graph now we press graph key. On the screen the graph of the polynomial function y is equal to x cube minus 5x square minus x plus 5 will appear on the coordinate axis. Now this is 10 by 10 viewing window. It means x axis are from minus 10 to 10 and y axis are also from minus 10 to 10. Now this is the standard window. Now to have a better view of the graph we can adjust this window. For this we press window key and the following screen will be displayed. Now let us discuss the window settings and their meanings. Now x min and x max are the leftmost and rightmost values to use on the x axis. Now if we enter x min is equal to minus 10 and x max is equal to 10 we are saying to use x values between x is equal to minus 10 and x is equal to 10 inclusive for the graph indicated on paper by using a closed interval from minus 10 to 10. Next xscle means scale of x axis it refers to the units to use on the x axis. If xscle is equal to 1 then each interval on the x axis is 1 unit. Also if xscle is equal to 3 then each interval on the x axis is 3 units. Now y min and y max are the smallest and largest values to use on the y axis. If we enter y min is equal to minus 10 and y max is equal to 10 we are saying to use y values between y is equal to minus 10 and y is equal to 10 inclusive for the graph indicated on paper by using a closed interval from minus 10 to 10. Now yscle refers to the units or scale to use on the y axis. Now if yscle is equal to 1 then each interval on the y axis is 1 unit. When writing our window information on paper we indicate the viewing window by stating x min x max by y min y max 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 2 to 6 by closed interval from minus 18 to 8. So we change the x min value to minus 2. 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. We scroll down and change x max value to 6. Similarly we write y min as minus 18 and y max as 8. Let us keep the scale as it is of 1 unit. Now we press graph key and we get the following display of graph. This window display is better than 10 by 10 window display. Thus choosing appropriate window gives better display of graph. Now we press trace to know the value those coordinates. Now if we place the cursor at this point then we get the coordinates as x is equal to 2 and y is equal to minus 9. Now we shall learn to find the roots of the equation x cube minus 5 x square minus x plus 5 is equal to 0 graphically. We know that roots or zeros of the function f of x are those points where f of x is equal to 0 that is on the graph the points of intersection of the curve with x axis will give us real zeros of the given function. We should note that only real zeros can be found using graph. Now if we see its graph we see that it intersects the x axis at three points so there are three real zeros for this equation. So now we find the zeros of this equation for this we press second key and then trace key we get this display we want to find zeros so we press number two key we get this display of graph. Now it is asking for left bound first we move the cursor to x axis intersecting point for left bound we move it down and press enter key the anchor will appear and now it is asking for right bound so we move up from this point and press enter key Now both anchor appears and it asks for yes so we press enter. Now on screen zero is displayed we get x is equal to minus one and c y is equal to zero so we can say that one zero is x is equal to minus one similarly we can find the other two zeros for this again we press second key followed by trace key and then number two key then by moving the cursor for lower and upper bounds at the other two intersecting points we will get the following displays and we can see we have other two real zeros as x is equal to one and x is equal to five so there are three zeros for this polynomial function that is x is equal to minus one one and five thus we can graph the polynomial equation by using appropriate windows and we can find its roots this completes our session hope you enjoyed this session