••.•´¯`•.•• ραяαвσℓαѕ ••.•´¯`•.••

Greetings, visitors of Mathland.~

How have you all been? I have been quite lovely myself. Today, I will be taking you all on a tour through the woods to go visit the March Hare at the Mad Hatter's tea party. Along the way, I will be reviewing the concepts of Parabolas and its equations with you all.

Starting off, the base equation for parabolas is:

(x-h)_­­­_­² = 4c (y-k)

Therefore:

Vertex: (h,k)

Focus: (h, k+c)

Directrix: y=k-c

A.O.S: x=h

In order to find the "c" value in this equation, one merely sets the number in the place of "4c" equal to '4c' and solve for "c". If the "c" is greater then zero, then the graph is facing upward. However, if the "c" is less then zero, then the graph is facing downwards.

Notes:

On the other hand, if the graph is opening to the left or right, the equation switches. It changes to:

(y-kh)_­­­_­² = 4c (x-h)

Meaning:

Vertex: (h,k)

Focus: (h+c, k)

Directrix: y=h-c

A.O.S: y=k

Notes:

To find the "c" of this equation, it is still the same exact process as finding the "c" of the other equation. Only in this situation, if c is greater then zero, then the graph opens right. I fc is less then zero, then the graph opens left.

That will be all for today!~ 

We will soon arrive at the Tea Party.~

See you next time.~