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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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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?


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?


    Homework
    Homework

    • NONE


    Warm up1
    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
    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.


    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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