Quadratic function can be written as:

- \(f : x \rightarrow ax^2 + bx + c\)
- \(f(x) = ax^2 + bx + c\)
- \(y = ax^2 + bx + c\)

Quadratic function can be drawn in Cartesian diagram as a parabolic like below:

**Concave-up parabolic curve**

The parabolic curve can be extended to the top left and the top right, hence the value of x can be **any number**.

The curve has minimum value of y, but it does not have maximum value (the curve can go up to infinite), hence the value of y must be greater or equal than \(y_{min}\).

**Concave-down parabolic curve**

The parabolic curve can be extended to the bottom left and the bottom right, hence the value of y can be **any number**.

The curve has maximum value of y, but it does not have minimum value (the curve can go down to infinite), hence the value of y must be less or equal than \(y_{max}\).

###### Domain and Range of Quadratic Function

**Domain**

\(x \in R\) or can be written as \(- \sim \: < x < +\sim\)

** Range for concave-up parabolic curve**

\(y \geq y_{min}\)

or can be written as

\(y_{min} \leq y < + \sim\)

**Range for concave-down parabolic curve**

\(y \leq y_{max}\)

or can be written as

\(- \sim \: < y \leq y_{max}\)

**Determine the maximum or minimum value of y of the function** \(y = ax^2 + bx + c\)

First, find the x value for maximum/minimum point, \(x_{min} = - \dfrac ba\)

Then substitute the value of \(x_{min}\) into \(y = ax^2 + bx + c\) to find the value of y.