Quadratic function

In algebra, a Quadratic function is a function that contains an expression where its degree (the highest exponent it has) is 2, which means that it is quadratic (See etymology). Its single-variable standard form isː

A quadratic graph with two real answers and no complex answers. Other quadratic graph have no real answers and 2 complex answers.

${\displaystyle f(x)=ax^{2}+bx+c}$

Where ${\displaystyle a}$, ${\displaystyle b}$ and ${\displaystyle c}$ are all constants and ${\displaystyle a}$ ≠ 0.

When such a function gets plotted on a graph where ${\displaystyle f(x)=y}$, a curve that extends infinitely called a parabola will appear.

When a quadratic function is set equal to zero, then it turns into a quadratic equation. The answers to the equation are where the function crosses the ${\displaystyle x}$-axis.

Etymology

The word quadratic comes from the Latin word quadrātum ("square"). This is because of the presence of a number (which is${\displaystyle x^{2}}$ in the standard form) that is the result of squaring its square root (${\displaystyle x\times x=x^{2}}$).