Warm Up

• Find the distance between the points• 1. (3,4)(6,7)• 2. (-3,7)(-7,3)

Algebra 3Chapter 10:Quadratic Relations and Conic

SectionsLesson 2: Parabolas

VOCAB

• Parabola - The set of all points equidistant from the focus and directrix–Focus lies on the axis of

symmetry–Directrix is perpendicular to the

axis of symmetry

Today

• Today we will focus on learning how to write the equation of a parabola when we know the focus and the vertex

• Tomorrow we will look at the graphs

Types• Standard Form with vertex (0,0)Equation Focus Directrix Axis Of

Symmetry

(0,p) y = -px = 0

(p,0) x = -py = 0

x 2 4 py

y 2 4 px

Directions

• Look at the focus or find the focus– This determines which formula to use

• Plug p into the equation• Solve

I DO (Parabola Equations)• Write an equation of the parabola

with the given focus/directrix and vertex at (0,0)• 1. (4,0) 5. y = 2• 2. (-2,0) 6. x = -5• 3. (-1/4 , 0) 7. x = -1/2• 4. (0,1) 8. y = -3

WE DO (Parabola Equations)•Write an equation of the parabola

with the given focus/directrix and vertex at (0,0)• 1. (0,4) 5. y = -1• 2. (0,-3) 6. x = 3/4• 3. (0,-4) 7. x = -4• 4. (5/12,0) 8. x = 2

YOU DO (Parabola Equations)•Write an equation of the parabola

with the given focus/directrix and vertex at (0,0)• 1. (-3 , 0) 5. y = 5/8• 2. (-5,0) 6. x = 6• 3. (0, 1/2) 7. y = 4• 4. (0,-3/8) 8. y = -1/12

Review

• Today you learned how to write the standard form of a parabola when you know the vertex and focus.

Homework

• Worksheet– 10.2B (13-20)

Warm Up

• Graph

Algebra 3Chapter 10:Quadratic Relations and Conic

SectionsLesson 2: Parabolas

Today

• Today we will look at the graphs of parabolas

Types• Standard Form with vertex (0,0)Equation Focus Directrix Axis Of

Symmetry

(0,p) y = -px = 0

(p,0) x = -py = 0

x 2 4 py

y 2 4 px

Graphing Knowledge

– If the number is positive graph makes a u• Opens up

– If the number is negative graph makes a n• Opens down

– If the number is positive graph makes a c• Opens right

– If the number is negative graph makes a backwards c• Opens left

Directions

• Solve the equation for the squared• Look at the equation– This determines which formula to use

• Solve for p• Find the focus• Find the directrix• Draw the graph

I DO (Graphing Parabolas)•Graph the quadratic•1. •2. •3. •4. •5.

WE DO (Graphing Parabolas)• Graph the quadratic• 1. • 2. • 3. • 4. • 5.

YOU DO (Graphing Parabolas)• Graph the quadratic• 1. x• 2. • 3. • 4. • 5.

Review

• Today you learned…

Homework

• Worksheet– 10.2 (1 – 12)