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

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

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

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?

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
- If it is ADDITION
- 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?

Homework

- NONE

Warm Up

- Name the 4 types of conic sections
- Explain how to classify a conic section

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.

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
- Find what your missing
- 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)

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