Quadratics – Vertex Form
The Vertex Form of a Quadratic Equation is y = a(x – h)² + k
The role of k
When k is positive, the graph is translated up.
When k is negative, the graph is translated down.
The role of h
When h is positive, the graph is translated to the right.
When h is negative, the graph is translated to the left.
Therefore, the vertex can be stated as (h, k).
The role of a
The graph is vertically stretched when a > 1 or a < -1.
The graph is vertically compressed when -1 < a < 1, a ≠ 0
Graphing a Quadratic Function
Once we have determined the vertex of a quadratic function we can use
something called “the step process” to find the points necessary to graph it.
The Step Process
Start at the vertex.
Move 1 right then a up/down, 1 right then 3a up/down, 1 right then 5a up/down, …
Move 1 left then a up/down, 1 left then 3a up/down, 1 left then 5a up/down, …
x and y-intercepts are useful when trying to graph any linear or non-linear function.
A quadratic function is a non-linear funcition
To find the x-intercept, set y=0 and solve for x.
To find the y-intercept, set x=0 and solve for y.
Y = x² - 4
y = x² + 2x - 8