UPSKILL MATH PLUS

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Let us discuss how to identify the graphs of a 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.