1. 2-1: Solving Equations
Graphically
© 2007 Roy L. Gover (www.mrgover.com)
Learning Goals:
•Solve equations using the
intersect method
•Solve equations using the
x-intercept method

2. Definition
A solution of an equation is
a number or numbers that
when substituted for the
variable in the equation
produces a true statement.
Two equations are
equivalent equations if they
have the same solutions.

3. Important Idea
Graphical solutions to
equations provide an
approximate solution when
algebraic methods are not
available to find an exact
solution.

4. Example
Find the approximate
solutions to the following
equation using the intersect
method:
2
1 2x x+ = +

5. Definition
To solve an equation of the
form by using the
intersection method:
( ) ( )f x g x=
1) Graph and1 ( )y f x=
2 ( )y g x= on the same screen.
2) Find the x coordinate of
each point of intersection.

6. Example
Find the approximate
solutions to the following
equation using the
intersect method:
2 3
3 5 2x x x x− − = − −

7. Try This
Find the approximate
solutions to the following
equation using the
intersect method:
2 3
4 3 6x x x x− − = + −

8. Solution
2 3
4 3 6x x x x− − = + −
Solution:
2.207x ≈

9. Important Idea
1) Go to Mode and
be sure calc is set
to FUNC
2) Go to Y=
3) Enter
equations (make
sure STATPLOT
is off)

10. Important Idea
4) Go to 2ND
CALC
5) Select 5: Intersect

11. Important Idea
6) Select point
of intersection.
7) Read approximate
solution

12. Try This
Find the approximate
solutions to the following
equation using the intersect
method:
4 2
3 1 4x x x+ − + =
x = -1.65,
2.03

13. Definition
The solution(s) to an
equation set equal to zero
is called a zero or root of
the equation. The solutions
are where the function
crosses the x axis and
y=0.

14. Definition
The x-intercept method of
solving an equation requires
these 3 steps:
1) Write the equation in the
equivalent form ( ) 0f x =
2) Graph ( )y f x=
3) Use 2nd
CALC 2:Zero

15. Example
Find the approximate
solutions to the following
equation using the x
intersect method:
2 3
4 3 6x x x x− − = + −

16. Try This
Find the approximate
solutions to the following
equation using the x
intersect method:
2
1x x− =
.618 , 1.618x = −

17. Example
Find the approximate
solutions to the following
equation using the x
intersect method:
2
2
2 1
0
9 9 2
x x
x x
+ −
=
− +

18. Important Idea
The values that make the
numerator zero make the
fraction 0. There is no need
to find the values that make
the denominator zero; these
values make the fraction
undefined.

19. Lesson Close
In our next lesson, we will
study methods of solving
equations algebraically.