Calculator Problems for Assignment #1

C.1 Graphing y=3x³ -5x²- 300x +300
^{At each stage sketch the graph you obtain. Always label your axes to show the scale (typing [WINDOW] will show you the x and y ranges).}
a) Plot the graph using the standard scale. (Press [Y=] and input the expression Y₁=3x³ - 5x² - 300x+300 then press [GRAPH], if you have changed the scale you can return to the standard scale using [ZOOM] [6:ZSTANDARD]).
b) Type [ZOOM], and move the cursor up or down until you find [0:ZoomFit], then type [ENTER]; a shortcut is just to type 0 after hitting [ZOOM]. ZoomFit automatically adjusts the y-scale so that the graph fits on the screen. Type [WINDOW] to see the new range of the y axis (making Yscl=100 may help your sketch).
c) Plot the graph from x=-5 to x=13 (Type [WINDOW], then input Xmin = -5, Xmax=13, the other settings can be left alone, but make sure that Xres =1. Use [ZOOM][0:ZOOMFIT] again as necessary to adjust the y range).
d) Adjust the x range until all three x-intercepts are nicely visible on the screen.

C.2 Finding Values
Find the values of y corresponding to x=3.2 and to x=-1.6 on the graph plotted in C1.
a) Type [TRACE] 3.2 [ENTER] and obtain the value of y at the bottom of the screen.
b) Type [2nd], [CALC], [1:value]. In the lower left corner you will see x= . Type [(-)]1.6 [ENTER].

C.3 Finding x-Intercepts
a) Plot the graph of x⁴ - 5x² + 3x -9 from x=-3 to x=3 (you should have two x intercepts visible)
b) Use [2nd][CALC][2:ZERO] to find the value of the right most intercept. (Use [TRACE] to move cursor to a value of x near to the intercept. Type [2nd][CALC], [2:ZERO]. The calculator will ask you for a Left Bound. Move cursor to the left of the intercept and type [ENTER]. The calculator will next ask you for a Right Bound. Move cursor to the right of the zero and type [ENTER]. Finally, the calculator will ask you for a Guess. Move cursor as close as you can to the zero and type [ENTER]. You should see x=2.3193869, y=0 on the screen. Thus the value of the intercept is (2.319,0) to 3 decimal places.
c) Repeat the process to find the other intercept.

C.4 Zooming In
Plot the graph of y=6x² - 17x +12
a) Use [ZOOM] [2:ZOOM IN] to blow up the region near to the origin where the graph just crosses (appears to touch) the x-axis (move the cursor to the region to be blown up and press [ENTER]). Repeat several times until you can clearly see the two x-intercepts. Sketch the graph (include the window settings to show the scale).
b) Use [2nd][CALC], [2:ZERO] to find the two x-intercepts.
c) Repeat part (a) using [ZOOM][1:ZBOX] (move the cursor to the position of one of the corners, press [ENTER], use the cursor to make the sides of the box around the region you want to blow up, press [ENTER]).