Date post: | 25-Dec-2015 |
Category: |
Documents |
Upload: | clementine-clark |
View: | 222 times |
Download: | 0 times |
Warm up!
The sun is a focus of earth’s orbit. Find an equation the models the
orbit of the Earth if all units are in millions of kilometers and the sun has a diameter of 1.4. You may
use a calculator.
And before we get to the learnin’, any
questions from your homework?
The Wørd
Section 9.1Parabolas
ParabolasSo I wanted a snow day
Wednesday…A parabola is the set of all points equidistant from a line called the directrix and a point called the
focus, not on the line.
Directrix
Focus
Vertex
Axis
The Derivation!
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
Parabolas cont.
…but then remembered that I take blue days off
anyways.
The equation of a parabola in standard form with vertex (h, k) is
given by:2
2
4 ( ) ( )
4 ( ) ( )
p y k x h OR
p x h y k
p is the distance from the vertex to the focus and from the vertex to
the directrix
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
So I wouldn’t want to miss…
2 8 0x y Graph the given
parabola.
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
2( 0) 8( 0)x y Graph the given
parabola.So I wouldn’t
want to miss…
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
2( 0) 8( 0)x y Graph the given
parabola.So I wouldn’t
want to miss…
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
…a blue day.28 4y x x
Graph the given parabola.
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
Graph the given parabola. 24 ( 2)y x
…a blue day.
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
Graph the given parabola. 24 ( 2)y x
…a blue day.
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
If we’re gonna have a day off…
2 4 6 2 0y y x Graph the given
parabola.
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
Graph the given parabola.2( 2) 6( 1)y x
If we’re gonna have a day off…
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
Graph the given parabola.2( 2) 6( 1)y x
If we’re gonna have a day off…
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
…it needs to be a red
day.21
( 2 5)4
y x x
Graph the given parabola.
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
Graph the given parabola. 21 4( 1)x y
…it needs to be a red
day.
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
Graph the given parabola. 21 4( 1)x y
…it needs to be a red
day.
THAT way…
Find the equation of the parabola in standard form.
10
8
6
4
2
-2
-4
-6
-8
-10
-10 -5 5 10
(5, 4)
(4.5, 4)
It’d make for an
easy work week!
Find the equation of the parabola in standard form.: ( 2, 0)
3: , 0
2
vertex
focus
‘Cause I’m
wicked lazy.
Find the equation of the parabola in standard form.: (0, 4)
: 2
vertex
directrix y
9.1 from your packet!And your homework!