9.4 Solving Quadratic Systems Precalculus 2015. Precalculus HWQ 3/21/13 Find the standard form of the equation of the hyperbola with vertices ( 2,3) and.

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Presentation transcript:

9.4 Solving Quadratic Systems Precalculus 2015

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).

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

Examples of Systems with One Solution

Examples of Systems with Two Solutions

Examples of a System with Three Solutions

Examples of a System with Four Solutions

Examples of Systems of Inequalities Solution

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

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

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

Algebraic solution to the system +

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

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:

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)

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)

Try solving the system algebraically: Solution:

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

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

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?

Homework: Pg odds