CALCULATOR GUIDE
To find an Intersection Point of two graphs using INTERSECTION or ISECT:
| To find an intersection point of two graphs on a TI-84:
With the two (or more) equations already graphed, press the 2ND CALC menu then INTERSECT. It asks, "First Curve?" press ENTER. "Second Curve?" press ENTER. It asks, "Guess?". Move the cursor near the intersection point and press ENTER. It should then give you the intersection point x=#, y=# :) If there is another intersection point to find, repeat these steps. |
| To find an intersection point of two graphs on a TI-86:
With the two (or more) equations already graphed, press MORE MATH MORE ISECT (that is the math on the screen, not the hard key). If there is only one intersection point you can ignore the questions it asks and press ENTER ENTER ENTER. If there are more than one intersection point, press ENTER ENTER then when it asks, "Guess?" move the cursor near the intersection point and press ENTER. It should then give you the intersection point x=#, y=# :) If there is second intersection point to find, press EXIT to get the graph menu back and repeat the steps above. |
| To find an intersection point of two graphs on a TI-89:
With the two (or more) equations already graphed, press F5 (the MATH menu) then INTERSECTION. It asks, "First Curve?" press ENTER. "Second Curve?" press ENTER. If there is another intersection point to find, repeat these steps. |
Example 1. Find the intersection point of the linear system below to the
nearest hundredth by graphing:
y = 2.6x - 3.2
y = (-2/3)x + 5/2
Graph the equations. You should get two lines intersecting in quadrant I. Use INTERSECTION to find their intersection point. The answer is (1.74, 1.34).
Example 2. Find the intersection points of the quadratic system below to the
nearest hundredth by graphing:
y = x2 - 1
y = -(x - 1)2 + 3
Graph the equations. You should get two parabolas one opening up, the other down. They intersect in 2 points, one in quadrant I, the other in quadrant III. Use INTERSECTION to find their intersection points. The answers are (1.82, 2.32) and (-0.82, -0.32).
Example 3. Solve x2 - 1 = -(x - 1)2 + 3 graphically.
Graph the left side as y1 = x2 - 1 and the right side as y2 = -(x - 1)2 + 3. The solution to the equation is the x-coordinate(s) of the intersection point(s) of these two curves. From example 2 we know that the solutions will be x = 1.82, -0.82.
The calculator will be particularly useful when the intersection point is some ugly decimal instead of a nice point. Try figuring out manually what the intersection points are in example 2 and you will really appreciate your calculator!
Originally written: 2000-05-08
Last revision:
2008-10-03 11:50 PM
