# The Basics

### Vertex Form Equation

## 𝑦 = 𝑎(𝑥 − ℎ) ^2 + k

What does each variable represent??? How can i transform my equation into a graph..?

## What does "a" represent?

"A" represents a number of things:

- It determines whether the parabola is vertically
**stretched or compressed**.

- If
**a**is less than -1 and less than 1, it is*compressed**(wider)*

Example: y= __0.5__(x-2)^2+4

- If
**a**is greater than -1 and 1, the parabola is*stretched (narrow)*

Example: y= __3__(x+4)^2-7

2. It determines the direction of the opening of the parabola

- If
**a**is*negative*, then the parabola is facing*downwards* - If
**a**is*positive*, the parabola will face*upwards*

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## What does "h" represent?

Unlike "a", "h" represents one thing.

It represents the **x coordinate **of the vertex. This means that it horizontally translates the parabola left or right.

BUT... it does not translate left or right according to the sign!

- If it is
**negative**, the parabola will translate to the RIGHT! - If it is
**positive**, the parabola will translate to the LEFT!

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## What does "k" represent?

Like "h", "k" represents one thing.

It represents the **y coordinate** of the vertex. This means that it horizontally translates the parabola up or down.

Unlike "h", it translates according to the sign!

- If "K" is
**negative**, the parabola will translate DOWN - If "K" is
**positive**, the parabola will translate UP

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