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 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 \((h,k)\).

A zero of a function is an input that results in an output of 0. In other words, if \(f(a) = 0\), then \(a\) is a zero of \(f\).