1. 9.4 Solving Quadratic Systems Precalculus 2015

2. Precalculus HWQ 3/21/13 Find the standard form of the equation of the hyperbola with vertices ( 2,3) and (2,-1) and foci (2,6) and (2,-4).

3. Objective: To classify conics and to solve systems of equations involving conics. Examples of Systems with No Solution

4. Examples of Systems with One Solution

5. Examples of Systems with Two Solutions

6. Examples of a System with Three Solutions

7. Examples of a System with Four Solutions

8. Examples of Systems of Inequalities Solution

10. Classify the conics and solve the system of equations. Draw the hyperbola: x y Graph line: (5, 3)

11. Solve the same system algebraically. Could we have used elimination? Solution:

12. Identify the conics in the system: 5x 2 + y 2 = 30 and -9x 2 + y 2 = 16. Try solving the system algebraically or graphically.

13. Algebraic solution to the system +

14. Graphical solution to the system. Draw ellipse. x y Draw hyperbola. (-1, 5) (1, 5) (-1, -5) (1, -5)

15. Identify the conics: x 2 + 4y 2 = 25 and 2y + x = 1 Try solving the system algebraically or graphically. Solve 2y + x = 1 for x. Solution:

16. Identify the conics in the system. Try solving the system algebraically or graphically: x 2 + y 2 −16x + 39 = 0 x 2 − y 2 −9 = 0 Solution: (3, 0), (5, 4), (5,−4)

17. Identify the conics in the system. Try solving the system algebraically or graphically: x 2 + 4y 2 − 4 = 0 −2y 2 + x + 2 = 0 Solution: (−2, 0), (0, 1), (0, −1)

18. Try solving the system algebraically: Solution:

19. Identify the conics in the system. Try solving the system algebraically or graphically: Solution:

20. x y Solve the system of inequalities. Graph parabola. Graph circle. The solution is the overlap of the two conics. solution

21. Share with your partner: Which method do you prefer when solving conics systems? Graphing or algebra? Why? When would the graphing method not be the best choice when solving a system?

22. Homework: Pg. 667 39-51 odds