Vertex Form Equation
𝑦 = 𝑎(𝑥 − ℎ) ^2 + k
What does "a" represent?
- 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
What does "h" represent?
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!
What does "k" represent?
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