C O N I CS E C T I O N S

Part 1: The Parabola

Parabola

Standard Form: y =ax2+bx+c

Vertex Form: y= a(x-h)2+k

Vertex:

a

bf

a

b

2

),

2

Vertex: (h,k)

How do you convert from Standard Form to Vertex Form?

Complete the Square!

Conic Sections part 1 of 4 : The Parabola

Directrix

Normal

Tangent

Point on the Parabola

Axis Of Symmetry

Focus

Vertex

Y- Axis

X- Axis

Roots; Zeros; Solutions

Conic Sections part 1 of 4 : The Parabola

Directrix

Axis Of Symmetry

Vertex

Focus

A parabola only has one focus. The focus will always fall on the axis of symmetry.

The distance from any point of the parabola to the Focus is equal to the distance from the point to the Directrix.

This means that vertex is the midpoint between the Focus and the Directrix

This means there is a slight modification that we can make to the Vertex Form that will help us ….

“m” is the distance between the Vertex and the Focus (or between the vertex and the directrix.)

khxay 2)(

ma

4

1

khxm

y 2)(4

1So ……

Let’s Play A Game!

Is this a Parabola?

YES!

No. These are hyperbolas.

YES!

YES! Parabolas can have a horizontal axis of symmetry!

Awwww ….

[censored]

Really, it’s not that bad. If you learned everything for a parabola with a vertical axis of symmetry, all you need to do is switch the x & y (and therefore the h & k since they represent the coordinated of the Vertex) for a parabola with a horizontal axis of symmetry.

khxm

y 2)(4

1Vertical axis of symmetry:

Horizontal axis of symmetry: hkym

x 2)(4

1

And that’s what you need to know about parabolas!

Looks like we are clear to try the assignment!