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

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-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

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-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

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-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

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-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

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-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

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-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!