9.4 solving quadratic systems precalculus 2015. precalculus hwq 3/21/13 find the standard form of...
DESCRIPTION
Objective: To classify conics and to solve systems of equations involving conics. Examples of Systems with No SolutionTRANSCRIPT
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9.4 Solving Quadratic 9.4 Solving Quadratic SystemsSystems
PrecalculusPrecalculus20152015
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Objective: To classify conics and to Objective: To classify conics and to solve systemssolve systems of equations involving conics. of equations involving conics.
Examples of Systems with No SolutionExamples of Systems with No Solution
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Examples of Systems with One SolutionExamples of Systems with One Solution
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Examples of Systems with Two SolutionsExamples of Systems with Two Solutions
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Examples of a System with Three SolutionsExamples of a System with Three Solutions
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Examples of a System with Four SolutionsExamples of a System with Four Solutions
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Examples of Systems of Inequalities
Solution
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Classify the conics and solve the system of Classify the conics and solve the system of equations.equations.x2 y2 16x y2
Draw the hyperbola:
x
y
Graph line:
(5, 3)2 2
116 16x y
2y x
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Solve the same system algebraically. Solve the same system algebraically. 2 2 16
2x yx y
2x y
2 22 16y y 2 24 4 16
4 12y y yy
35
yx
5, 3 Could we have used elimination?Solution:
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Identify the conics in the system: Identify the conics in the system:
55xx22 + + yy2 2 = 30 and -9= 30 and -9xx22 + + yy2 2 = 16. = 16.
Try solving the system algebraically or Try solving the system algebraically or graphically.graphically.
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Algebraic solution to the systemAlgebraic solution to the system
5x2 y2 30
9x2 y2 1614x2 14x 1
2 2 015 3 yy5
1, 5 1, 5 1,5 1, 5
+
5x2 y2 30
9x2 y2 16
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Graphical solution to the system.Graphical solution to the system.5x2 y2 30
9x2 y2 16
Draw ellipse.
x
y
Draw hyperbola.
(-1, 5)x2
6y2
301
y2
16
9x2
161
(1, 5)
(-1, -5) (1, -5)
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Identify the conics: Identify the conics: xx22 + 4 + 4yy2 2 = 25 and 2= 25 and 2yy + + xx = 1 = 1 Try solving the system algebraically or Try solving the system algebraically or graphically.graphically.
1 2 x ySolve 2y + x = 1 for x.
2 24 25 yx 2 24 22 51 yy
8y2 4y 24 04(2y 3)(y 2) 0
y32
y2 34, 3,2 2
Solution:
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Identify the conics in the system.Identify the conics in the system.Try solving the system algebraically or Try solving the system algebraically or graphically:graphically:x2 + y2 −16x + 39 = 0x2 − y2 −9 = 0
Solution:
(3, 0), (5, 4), (5,−4)
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Identify the conics in the system.Identify the conics in the system.Try solving the system algebraically or Try solving the system algebraically or graphically:graphically: x2 + 4y2 − 4 = 0−2y2 + x + 2 = 0
Solution:
(−2, 0), (0, 1), (0, −1)
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Try solving the system algebraically:Try solving the system algebraically:
2 25 2 5 12 01 0
x xy yx y
3 30 3 30 3 30 3 30, , ,6 6 6 6
Solution:
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Identify the conics in the system.Identify the conics in the system.Try solving the system algebraically or Try solving the system algebraically or graphically:graphically:
2 2
2
4 4 8 4 0
4 4 0
x y x y
x y
0,1 , 2,0Solution:
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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?
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Homework:Homework:Pg. 667 39-51 odds