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:


  1. 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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Here is a visual of a vertex form equation

Big image