General Mathematics: Quadratic Functions and Their Applications

Vocabulary flashcards covering the definitions, standard and vertex forms, key characteristics, domain, range, and graphical features of quadratic functions.

Quadratic Function

A type of polynomial function of degree two, written in the form $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers and $a \neq 0$.

Parabola

The curve that forms the graph of a quadratic function, which opens upward if $a > 0$ or downward if $a < 0$.

Standard Form of a Quadratic Function

The algebraic representation of a quadratic function given by $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers and $a \neq 0$.

Vertex Form of a Quadratic Function

The representation given by $f(x) = a(x - h)^2 + k$, which directly indicates the vertex of the parabola at $(h, k)$.

Vertex

The turning point and either the highest or lowest point of a parabola, designated as $V(h, k)$ or found using the coordinate $x = -\frac{b}{2a}$.

Axis of Symmetry

The vertical line $x = h$ that passes through the vertex and divides the parabola into two symmetrical halves.

Minimum Point

The lowest point of a parabola located at the vertex, occurring when the leading coefficient $a > 0$ such that the function reaches a minimum value of $f(x) = k$.

Maximum Point

The highest point of a parabola located at the vertex, occurring when the leading coefficient $a < 0$ such that the function reaches a maximum value of $f(x) = k$.

Domain of a Quadratic Function

The set of all real numbers, expressed in interval notation as $(-\infty, \infty)$, because the function is defined for every real value of $x$.

Range of a Quadratic Function

The set of all possible output values of the function, given by $[k, \infty)$ if the parabola opens upward ($a > 0$) or $(-\infty, k]$ if the parabola opens downward ($a < 0$).

$y$-intercept

The point where the graph of a quadratic function crosses the $y$-axis.

$x$-intercepts

The values of $x$ (also known as roots) for which $f(x) = 0$, representing where the graph crosses the $x$-axis.