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# Hprec2 1

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### Hprec2 1

1. 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. 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. 3. Important Idea Graphical solutions to equations provide an approximate solution when algebraic methods are not available to find an exact solution.
4. 4. Example Find the approximate solutions to the following equation using the intersect method: 2 1 2x x+ = +
5. 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. 6. Example Find the approximate solutions to the following equation using the intersect method: 2 3 3 5 2x x x x− − = − −
7. 7. Try This Find the approximate solutions to the following equation using the intersect method: 2 3 4 3 6x x x x− − = + −
8. 8. Solution 2 3 4 3 6x x x x− − = + − Solution: 2.207x ≈
9. 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. 10. Important Idea 4) Go to 2ND CALC 5) Select 5: Intersect
11. 11. Important Idea 6) Select point of intersection. 7) Read approximate solution
12. 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. 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. 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. 15. Example Find the approximate solutions to the following equation using the x intersect method: 2 3 4 3 6x x x x− − = + −
16. 16. Try This Find the approximate solutions to the following equation using the x intersect method: 2 1x x− = .618 , 1.618x = −
17. 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. 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. 19. Lesson Close In our next lesson, we will study methods of solving equations algebraically.