# 10.1: Quadratic Functions and Their Graphs

Difficulty Level: Basic Created by: CK-12
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TermDefinition
$x$-intercept of a parabola As with linear equations, the $x$-intercepts of a parabola are where the graph intersects the $x$-axis. The $y$-value is zero at the $x$-intercepts.
leading coefficient of a parabola The variable $a$ in the equation $y=ax^2+bx+c$ is called the leading coefficient of the quadratic equation.
minimums and maximums of a parabola An equation of the form $y=ax^2+bx+c$ forms a parabola. If $a$ is positive, the parabola will open upward. The vertex will be a minimum. If $a$ is negative, the parabola will open downward. The vertex will be a maximum.
symmetry of a parabola A parabola can be divided in half by a vertical line. Because of this, parabolas have symmetry. The vertical line dividing the parabola into two equal portions is called the line of symmetry.
vertex of a parabola All parabolas have a vertex, the ordered pair that represents the bottom (or the top) of the curve. The line of symmetry always goes through the vertex. The vertex of a parabola is the ordered pair $(h, k)$.
Coefficient A coefficient is the number in front of a variable.
Dilation To reduce or enlarge a figure according to a scale factor is a dilation.
domain The domain of a function is the set of $x$-values for which the function is defined.
Horizontal shift A horizontal shift is the result of adding a constant term to the function inside the parentheses. A positive term results in a shift to the left and a negative term in a shift to the right.
Parabola A parabola is the characteristic shape of a quadratic function graph, resembling a "U".
quadratic function A quadratic function is a function that can be written in the form $f(x)=ax^2 + bx + c$, where $a$, $b$, and $c$ are real constants and $a\ne 0$.
standard form The standard form of a quadratic function is $f(x)=ax^{2}+bx+c$.
Symmetry A figure has symmetry if it can be transformed and still look the same.
Vertex The vertex of a parabola is the highest or lowest point on the graph of a parabola. The vertex is the maximum point of a parabola that opens downward and the minimum point of a parabola that opens upward.
vertical axis The vertical axis is also referred to as the $y$-axis of a coordinate graph. By convention, we graph the output variable on the $y$-axis.

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