Identifying the graphs of quadratic function — lesson. Mathematics State Board, Class 10.

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Let us discuss how to identify the graphs of a quadratic function.

Quadratic function:

A function

$f: \mathbb{R} \rightarrow \mathbb{R}$ defined by

$f(x) = ax^2 + bx + c$ ,

$a \neq 0$ is called a quadratic function.

Let us further discuss some specific quadratic functions.

Specification 1:

A quadratic function

$f: \mathbb{R} \rightarrow \mathbb{R}$ with domain

$x \in \mathbb{R}$ and range

$f(x) \in [0, \infty)$ is defined by

$f(x) = x^2$ .

The graphical representation of this quadratic function is given by:

Specification II:

A function

$f: \mathbb{R} \rightarrow \mathbb{R}$ defined by

$f(x) = - x^2$ is a quadratic function with a domain

$x \in \mathbb{R}$ and a range

$f(x) \in (- \infty, 0]$ .

The graphical representation of the quadratic function is given by:

Important!

The quadratic functions are not one-to-one functions.
The equation of motion of the particle travelling under the influence of gravity is an example of the quadratic function of time.

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5. Identifying the graphs of quadratic function