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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
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?
slide2

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

vocab
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
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
Formulas
  • Parabola
      • or
  • Circle
  • Ellipse
      • or
  • Hyperbola
      • or
directions
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
i do classifying
I DO (Classifying)
  • Classify the conic section
  • 1.
  • 2.
  • 3.
  • 4.
we do classifying
WE DO (Classifying)
  • Classify the conic section
  • 1.
  • 2.
  • 3.
  • 4.
you do classifying
YOU DO (Classifying)
  • Classify the conic section
  • 1.
  • 2.
  • 3.
  • 4.
review
Review
  • What did you learn today?
warm up1
Warm Up
  • Name the 4 types of conic sections
  • Explain how to classify a conic section
slide13

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

classifying discriminant
Classifying – discriminant
  • Today we are going to learn one way to classify a conic section. This way is to find the discriminant
formulas1
Formulas
  • General Equation
  • Discriminant
knowledge
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
directions1
DIRECTIONS
  • Find a, b, c
  • Find the discriminant
  • Classify the conic
i do classifying1
I DO (Classifying)
  • Classify the conic section
  • 1.
  • 2.
  • 3.
  • 4.
we do classifying1
WE DO (Classifying)
  • Classify the conic section
  • 1.
  • 2.
  • 3.
  • 4.
you do classifying1
YOU DO (Classifying)
  • Classify the conic section
  • 1.
  • 2.
  • 3.
  • 4.
review1
Review
  • What did you learn today?
homework1
HOMEWORK
  • Worksheet
    • 10.6B (9 – 14)
warm up2
Warm Up
  • Classify the conic
  • 1.
  • 2.
slide24

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

today
TODAY
  • Today we are going to learn how to write equations of conics that are NOT in the center of a graph
formulas2
Formulas
  • Parabola
      • or
  • Circle
  • Ellipse
      • or
  • Hyperbola
      • or
center
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
directions2
Directions
  • Label what you know
  • Find what your missing
    • A, b, c, p, h, k
  • Plug into the
i do equations
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
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
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)
review2
Review
  • Today you learned how to write the equation of a translated conic
homework2
HOMEWORK
  • Worksheet
    • 10.6B (1 – 4)
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