Fundamentals of Quadratic Functions

A quadratic function's graph crosses the x-axis at points known as its ______ or ______.

The solutions to a quadratic equation, which can be either real or complex, are found using the ______ ______.

The ______ of the parabola is the graph's peak or trough and is calculated by the formula ______.

In the vertex form of a quadratic function, f(x) = a(x - h)^2 + k, the coordinates (h, k) represent the ______.

To find the highest or lowest point on a quadratic function's graph, one can also use the method of ______ the ______.

Standard Form of Quadratic Function

Factored Form and Roots

Vertex Form and Vertex Location

The shape of a ______ function is a parabola, which is characterized by its curvature, orientation, and placement.

The ______ coefficient 'a' dictates whether the parabola opens ______ or downward and its ______.

The vertex, direction, and ______ of a parabola can be determined by its coefficients, which are essential for ______ the function.

If the leading coefficient 'a' is ______, the parabola opens ______, and its steepness is affected by the ______ value of 'a'.

A negative 'a' value causes the parabola to open ______, and the ______ of 'a' influences how steep the parabola is.

Bivariate quadratic function general form

Intersections of bivariate quadratic functions with plane z=0

Quadric surfaces in three-dimensional space

When quadratic functions are ______ to their outputs, they can exhibit ______ behavior.