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 Sections

Lesson 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– 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

Algebra 3Chapter 10: Quadratic

Relations and Conic Sections

Lesson 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 Sections

Lesson 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• 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)