C.3.4.:  5:intersect

1. Find the intersection point(s) of 2 or more graphs.

a) To find the intersection(s) of two graphs: i.e.  y = (1/20)x3 – 3  and  y = -x2 + 1

1.)    Enter the two equations in  Y=

2.)    GRAPH

3.)    Use the 5:intersect function to find the point of intersection(s) between the two graphs.

a)      2nd CALC

b)      5:intersect

c)      First Curve? Move cursor to the left of the intersection point you wish to find and press ENTER

d)      Second Curve? ENTER.

e)      The cursor will jump to the other curve. Guess? will appear then press ENTER

f)        Intersection will appear and the coordinates of the intersection point are shown:  X=-2.115  Y=-3.473

g)      Repeat for multiple intersection points     (a)  & (b)                (c)                            (d)                       (e)                      (f)

1b)  Find the other intersection point of the two curves above:

Answer:   Intersection point is (1.911, -2.651)

Practice:  Find the intersection point of the two graphs:   y = -x2 – 4x – 2  and  y = x2 + 2x -1

Answer:  Intersection points are (-.177, -1.323) and (-2.823, 1.323).

2.  The 5:intersect option can also be used to find the x-intercepts of a graph.

a) Find the x-intercepts of the graph:  y = x2 + 2x + 1.  Hint: Use y = 0 for the other equation.

1.)  Enter the two equations in  Y=

2.)     Graph

3.)     Use the 5:intersect function to find the point of intersection(s) between the two graphs.

a)      2nd CALC

b)      5:intersect

c)      First Curve?  ENTER

d)      Second Curve? ENTER.

e)      Guess? will appear then press, Move cursor near the intersection in question, press ENTER

f)        Intersection will appear and the coordinates of the intersection point are shown:  X=-1.0  Y=0

g)      Repeat for multiple intersection points

Practice:  Find the intersection point(s) of the graphs:   y = x2 + 7x + 6.

The points you will find are also called solutions to the equation and can be used for factoring.

Answer:  Intersection points are (-6, 0) and (-1, 0).