TI-84 Plus CE field manual for IB Math
Finding intersections
Plot two functions and read every intersection by zooming to standard, zooming out until the crossings fit, then drawing a Zoom Box around the cluster and using the calculator's intersect tool.
Find every intersection of y1=ex(x2−11x+30) and y2=(x−8)2.
Press and enter both functions. On Y1 type ; press to Y2 and type .
Frame the curves in the standard window: press (6: ZStandard). Two crossings show up on the right side of the screen (around x ≈ 5 and x ≈ 6), but the exponential rockets off the top before x = 1, so there's no way to tell from this view whether more intersections sit above the visible window.
Pull the camera back so the crossings come into view. Press (3: Zoom Out); when the cursor appears, press to zoom out, then a second time to zoom out again. Each press multiplies the visible window by the XFact/YFact factors set in ZOOM→MEMORY→4: SetFactors (default 4). Two zooms expand the window to [-160, 160] × [-160, 160]; all three intersections are now on screen, packed near the centre.
Tighten the window around just the crossings: press (1: Box). Use the arrow keys to move the cursor to the upper-left of the cluster and press to anchor the first corner. Move the cursor to the lower-right and press again to set the second corner. The dashed marquee shows the region you've selected.
The window snaps to the box and the three crossings are clearly separated. Now read each one off precisely: press (5: intersect). At First curve? press ; at Second curve? press again; at Guess? use / to move the cursor near one intersection, then press . The calculator jumps to the intersection and reports X= and Y=. Repeat for each of the three crossings.
The three intersections are approximately (0.876,50.7), (4.94,9.38), and (6.01,3.96).
Your turn
Work each one on your calculator, then check the answer.
- 1
Find all intersections of f(x)=ex/2 and g(x)=x2−3.
- 2
Find all intersections of f(x)=ln(x) and g(x)=0.02x2.
- 3
Find all intersections of f(x)=8sin(x) and g(x)=4x2−5.