Quadratic functions can be written in this form:

[ f(x) = ax^2 + bx + c ]

They have some important parts called domain and range. Let's break it down:

• Domain: This is the set of all possible input values for the function. For quadratic functions, the domain is all real numbers. We can show this as $(-\infty, \infty)$. That means you can pick any number to plug into the function!

• Range: The range tells us the possible output values of the function, and it depends on the value of ( a ):

  • If ( a > 0 ), the range starts from the vertex's ( y )-coordinate (let’s call it ( k )) and goes up. We can write this as ([k, \infty)).
  • If ( a < 0 ), the range goes down from ( k ). This is shown as ((-\infty, k]).

• Vertex: The vertex is a special point on the graph. It is either the highest or lowest point of the function. This point is really important because it helps us determine the range.

So, to sum up, the way the graphs of quadratic functions behave is linked to their domain and range, and the vertex plays a key role in it!