Unit 4
Glossary
Integrated Math 2
A directrix is the line that, together with a point called the focus, defines a parabola.
This diagram shows a parabola is the set of points equidistant from the focus and directrix.
A quadratic expression is in factored form when it is written as the product of a constant times two linear factors.
- \(2x^2 + 4x - 6\) written in factored form is \(2(x-1)(x+3)\).
- \(15x^2 + x - 2\) written in factored form is \((5x + 2)(3x-1)\).
A focus is the point that, together with a line called the directrix, defines a parabola.
This diagram shows a parabola is the set of points equidistant from the focus and directrix.
A parabola is the set of points that are equidistant from a given point, called the focus, and a given line, called the directrix.
A quadratic expression is an expression that is equivalent to one of the form \(ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).
A quadratic function is a function where the output is given by a quadratic expression in the input.
For example, \(f(x) =ax^2+bx+c\), where \(a\), \(b\), and \(c\) are constants and \(a\ne0\), is a quadratic function.
The standard form of a quadratic expression is \(ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(a\) \(\ne\) 0.
The vertex of the graph of a quadratic function or of an absolute value function is the point where the graph changes from increasing to decreasing, or vice versa. It is the highest or lowest point on the graph.
The vertex form of a quadratic expression is \(a(x-h)^2 + k\), where \(a\), \(h\), and \(k\) are constants and \(a \neq 0\). The vertex of the graph is at the point \((h,k)\).