find the equation of the parabola with the given features. graph the parabola.

1.Vertex (0,0) focus (0,3)

and

2. (0,0) directrix x+1=0

Both of them confuse me. can someone explain it step by step please!!!

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- July 20th 2006, 09:49 PMmattballer082i dont get it!! ahhh! help
find the equation of the parabola with the given features. graph the parabola.

1.Vertex (0,0) focus (0,3)

and

2. (0,0) directrix x+1=0

Both of them confuse me. can someone explain it step by step please!!! - July 20th 2006, 11:33 PMCaptainBlackQuote:

Originally Posted by**mattballer082**

have in your first problem) with vertex , and focus has directrix

, and equation:

In your first question the vertex is at so , and as the focus

is at so , and the equation becomes:

In your second problem the symetry axis is horizontal, so what I will do

is derive the equation as though it were vertical and finaly interchenge and .

Flipping the axis leaves the vertex at but the directrix becomes

or equivalently

In this case and so the equation

for the vertical axis parabola is:

,

and interchanging and gives us:

for the horizontal axis parabola.

RonL - July 21st 2006, 07:45 AMSoroban
Hello, mattballer082!

These problems have the vertex at the origin.

There are two types:

. . . . . the parabola opens up or down: or

. . . . . the parabola opens right or left: or

is the distance from the Vertex to the Focus

. . and the distance from the Vertex to the Directrix.

Note: the curve always bends "around the Focus" and "away from the Directrix".

Quote:

Find the equation of the parabola with the given features.

Graph the parabola.

1. Vertex (0,0), focus (0,3)

Make a sketch.Code:`|`

* Fo(0,3) *

* | *

* | *

- - - o - - -

V|(0,0)

Plot the Vertex and the Focus.

We know that the parabola bends*around the Focus,*

. . so we know its orientation: opens upward.

We use the form: .

We see that

. . Therefore, the equation is: .

Quote:

2. Vertex (0,0), directrix x + 1 = 0

The vertex is at the origin; the directrix is the vertical line:Code:`: | *`

: | *

: |*

- - + - o - - - - - - -

: |*

: | *

: | *

x=-1

Plot the Vertex and the Directrix.

We the know the parabola "bends away from the directrix"

. . so we know its orientation: opens right.

We use the form: .

We see that

. . Therefore, the equation is: .