Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)
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Transcript of Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)
![Page 1: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/1.jpg)
Warm Up
• Find the distance between the points• 1. (3,4)(6,7)• 2. (-3,7)(-7,3)
![Page 2: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/2.jpg)
Algebra 3Chapter 10:Quadratic Relations and Conic
SectionsLesson 2: Parabolas
![Page 3: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/3.jpg)
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
![Page 4: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/4.jpg)
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
![Page 5: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/5.jpg)
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
![Page 6: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/6.jpg)
Directions
• Look at the focus or find the focus– This determines which formula to use
• Plug p into the equation• Solve
![Page 7: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/7.jpg)
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
![Page 8: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/8.jpg)
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
![Page 9: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/9.jpg)
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
![Page 10: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/10.jpg)
Review
• Today you learned how to write the standard form of a parabola when you know the vertex and focus.
![Page 11: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/11.jpg)
Homework
• Worksheet– 10.2B (13-20)
![Page 12: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/12.jpg)
Warm Up
• Graph
![Page 13: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/13.jpg)
Algebra 3Chapter 10:Quadratic Relations and Conic
SectionsLesson 2: Parabolas
![Page 14: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/14.jpg)
Today
• Today we will look at the graphs of parabolas
![Page 15: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/15.jpg)
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
![Page 16: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/16.jpg)
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
![Page 17: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/17.jpg)
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
![Page 18: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/18.jpg)
I DO (Graphing Parabolas)•Graph the quadratic•1. •2. •3. •4. •5.
![Page 19: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/19.jpg)
WE DO (Graphing Parabolas)• Graph the quadratic• 1. • 2. • 3. • 4. • 5.
![Page 20: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/20.jpg)
YOU DO (Graphing Parabolas)• Graph the quadratic• 1. x• 2. • 3. • 4. • 5.
![Page 21: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/21.jpg)
Review
• Today you learned…
![Page 22: Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)](https://reader035.fdocuments.us/reader035/viewer/2022081521/5a4d1bae7f8b9ab0599cb98f/html5/thumbnails/22.jpg)
Homework
• Worksheet– 10.2 (1 – 12)