Finding the Maximum or Minimum of a Quadratic Function

Vocabulary terms and definitions covering quadratic functions, parabolas, and determining maximum and minimum values using the vertex.

Parabola

The graph of a quadratic function.

Quadratic Function

A function that can be expressed in the form $g(x) = ax^2 + bx + c$, whose graph is a parabola.

Downward-Opening Parabola

A parabola whose leading coefficient $a$ is negative, indicating that the quadratic function has a maximum value.

Upward-Opening Parabola

A parabola that opens upward, indicating that the quadratic function has a minimum value.

Vertex of a Parabola

The point on the parabola that tells whether the function has a maximum or minimum value, the location where it occurs, and the value itself.

Vertex Formula ($x$-coordinate)

The formula $x = -\frac{b}{2a}$, used to find the $x$-coordinate of the vertex of a quadratic function.

Location of Maximum or Minimum Value

The $x$-coordinate of the vertex, indicating the input value where the function's extremum occurs.

Maximum or Minimum Value

The $y$-coordinate of the vertex, calculated by evaluating the quadratic function at the vertex's $x$-coordinate.