Unit 9 Quadratic Functions

Domain of a Quadratic Equation

All Real Numbers, because the legs of the parabola continue to move outward, left and right, for infinity.

Range of a Quadratic Equation

An inequality that states the movement of the parabola up or down the y-axis.

Quadratic Function

Any function that can be written in the form y=ax^2+bx+c, where a, b, and c are all real numbers and a does not equal 0.

Maximum

On a parabola that opens downward, the y-coordinate of the vertex is called the...

Minimum

On a parabola that opens upward, the y-coordinate of the vertex is called the...

Ways to name the Solutions of a Quadratic Function.

Solutions, Zeros of a Function, Roots of a Function, x-Intercepts.

Parabola

The graph of a quadratic function.

Vertex

The highest or lowest point on a parabola.

Graph of a Quadratic Function with TWO SOLUTIONS.

The legs of the parabola both cross over the x-Axis.

Graph of a Quadratic Function with NO SOLUTION.

The parabola does not cross over the x-Axis.

Parent Function

The simplest function in a family; all functions in the family are transformations of it.

Graph of a Quadratic Function with ONE SOLUTION.

The vertex of the parabola is the only point on the graph that touches the x-Axis.

Axis of Symmetry

The vertical line that divides the parabola in half.

Solution

The x-intercept(s) of the quadratic equation

Zero of a Function

The x-value that makes the function equal to zero. It is the same as the x-intercept of a function.

Quadratic Parent Function

y = x^2; it is a u shape on the origin of the coordinate plane

Roots

X-intercepts, solutions or zeros of a quadratic function are also called...

Possible Types of Solutions to a Quadratic Function

3 Possible Types of Solutions: NO SOLUTION, ONE SOLUTION, or TWO SOLUTIONS

Downward-opening parabola

When the "a" value is negative.

Upward-opening parabola

When the "a" value is positive