warm up
DESCRIPTION
Warm Up. What is the standard form of a parabola? What is the standard form of a circle? What is the standard form of a ellipse? What is the standard form of a hyperbola?. Algebra 3 Chapter 10: Quadratic Relations and Conic Sections Lesson 6: Graphing and Classifying Conics. VOCAB. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062811/56816134550346895dd08e72/html5/thumbnails/1.jpg)
Warm Up
• What is the standard form of a parabola?• What is the standard form of a circle?• What is the standard form of a ellipse?• What is the standard form of a hyperbola?
![Page 2: Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062811/56816134550346895dd08e72/html5/thumbnails/2.jpg)
Algebra 3Chapter 10: Quadratic
Relations and Conic Sections
Lesson 6: Graphing and Classifying Conics
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VOCAB• Conics or Conic Sections – parabolas,
circles, ellipses, and hyperbolas…basically all curves that are formed by the intersections of a plane and a double-napped cone• Discriminant – an equation that can
tell what type of conic you have
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Classifying – way 1
• Today we are going to learn one way to classify a conic section. This way is to put it in a normal formula.
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Formulas• Parabola
• or
• Circle
• Ellipse• or
• Hyperbola• or
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Directions
• Look at the powers of x and y– If ONLY one of them is squared…parabola
• Get x and y on the same side• Divide by the number– If it is SUBTRACTION…Hyperbola– If it is ADDITION• Denominators are the same…Circle• Denominators are different…Ellipse
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I DO (Classifying)
•Classify the conic section•1. •2. •3. •4.
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WE DO (Classifying)
•Classify the conic section•1. •2. •3. •4.
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YOU DO (Classifying)
•Classify the conic section•1. •2. •3. •4.
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Review
• What did you learn today?
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Homework
• NONE
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Warm Up
• Name the 4 types of conic sections• Explain how to classify a conic section
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Algebra 3Chapter 10: Quadratic
Relations and Conic Sections
Lesson 6: Graphing and Classifying Conics
![Page 14: Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062811/56816134550346895dd08e72/html5/thumbnails/14.jpg)
Classifying – discriminant
• Today we are going to learn one way to classify a conic section. This way is to find the discriminant
![Page 15: Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062811/56816134550346895dd08e72/html5/thumbnails/15.jpg)
Formulas• General Equation
• Discriminant
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KNOWLEDGE• Discriminant–Less than zero•B = 0 and A = C …it’s a circle•B ≠ 0 or A ≠ C … it’s an ellipse
–Equal zero• It’s a parabola
–Greater than zero• It’s a hyperbola
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DIRECTIONS
• Find a, b, c• Find the discriminant• Classify the conic
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I DO (Classifying)• Classify the conic section• 1. • 2. • 3. • 4.
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WE DO (Classifying)• Classify the conic section• 1. • 2. • 3. • 4.
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YOU DO (Classifying)• Classify the conic section• 1. • 2. • 3. • 4.
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Review
• What did you learn today?
![Page 22: Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062811/56816134550346895dd08e72/html5/thumbnails/22.jpg)
HOMEWORK
• Worksheet– 10.6B (9 – 14)
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Warm Up
• Classify the conic• 1. • 2.
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Algebra 3Chapter 10: Quadratic
Relations and Conic Sections
Lesson 6: Graphing and Classifying Conics
![Page 25: Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062811/56816134550346895dd08e72/html5/thumbnails/25.jpg)
TODAY
• Today we are going to learn how to write equations of conics that are NOT in the center of a graph
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Formulas• Parabola
• or
• Circle
• Ellipse• or
• Hyperbola• or
![Page 27: Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062811/56816134550346895dd08e72/html5/thumbnails/27.jpg)
CENTER
• Center of all shapes is• (h , k)• A is the distance from the vertex to the center• C is the distance from the focus to the center
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Directions
• Label what you know• Find what your missing– A, b, c, p, h, k
• Plug into the
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I DO (Equations)• Write the equation of the conic section• 1. Parabola … V (-2, 1) F (-3, 1)• 2. Circle … Center (3, -2) r = 4• 3. Ellipse … F (3, 5) (3, -1) V (3, 6) (3, -2)• 4. Hyperbola … V (5, -4) (5, 4) F (5, -6) (5, 6)
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WE DO (Equations)• Write the equation of the conic section• 1. Parabola … V (1, -2) F (1, 1)• 2. Circle … Center (9, 3) r = 4• 3. Ellipse … V(2, -3) (2, 6) F (2, 0) (2, 3)• 4. Hyperbola … V (-4, 2) (1, 2) F (-7, 2) (4, 2)
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YOU DO (Equations)• Write the equation of the conic section• 1. Parabola … V (-3, 1) directrix x = -8• 2. Circle … Center (-4, 2) r = 3• 3. Ellipse … F (-2, 2) (4, 2) CV (1, 1 (1, 3)• 4. Hyperbola … V (8, -4) (8, 4) F (8, -6) (8, 6)
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Review
• Today you learned how to write the equation of a translated conic
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HOMEWORK
• Worksheet– 10.6B (1 – 4)