Warm Up

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# Warm Up - PowerPoint PPT Presentation

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.

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Presentation Transcript
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 3Chapter 10: Quadratic Relations and Conic SectionsLesson 6: Graphing and Classifying Conics

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
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.
Formulas
• Parabola
• or
• Circle
• Ellipse
• or
• Hyperbola
• or
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
• Denominators are the same…Circle
• Denominators are different…Ellipse
I DO (Classifying)
• Classify the conic section
• 1.
• 2.
• 3.
• 4.
WE DO (Classifying)
• Classify the conic section
• 1.
• 2.
• 3.
• 4.
YOU DO (Classifying)
• Classify the conic section
• 1.
• 2.
• 3.
• 4.
Review
• What did you learn today?
Warm Up
• Name the 4 types of conic sections
• Explain how to classify a conic section

### Algebra 3Chapter 10: Quadratic Relations and Conic SectionsLesson 6: Graphing and Classifying Conics

Classifying – discriminant
• Today we are going to learn one way to classify a conic section. This way is to find the discriminant
Formulas
• General Equation
• Discriminant
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
DIRECTIONS
• Find a, b, c
• Find the discriminant
• Classify the conic
I DO (Classifying)
• Classify the conic section
• 1.
• 2.
• 3.
• 4.
WE DO (Classifying)
• Classify the conic section
• 1.
• 2.
• 3.
• 4.
YOU DO (Classifying)
• Classify the conic section
• 1.
• 2.
• 3.
• 4.
Review
• What did you learn today?
HOMEWORK
• Worksheet
• 10.6B (9 – 14)
Warm Up
• Classify the conic
• 1.
• 2.

### Algebra 3Chapter 10: Quadratic Relations and Conic SectionsLesson 6: Graphing and Classifying Conics

TODAY
• Today we are going to learn how to write equations of conics that are NOT in the center of a graph
Formulas
• Parabola
• or
• Circle
• Ellipse
• or
• Hyperbola
• or
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
Directions
• Label what you know
• A, b, c, p, h, k
• Plug into the
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)
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)
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)
Review
• Today you learned how to write the equation of a translated conic
HOMEWORK
• Worksheet
• 10.6B (1 – 4)