Quadratic Functions

Relation

A set of ordered pairs

Domain

All the x-values included in the parabola. Always go LEFT to RIGHT (always negative infinity to infinity)

Range

All the y-values included in the parabola. Always go BOTTOM to TOP

Increasing and decreasing interval

Always go left to right- where the graph begins increasing and where the graph begins decreasing. Always use domain values

Axis of symmetry

Always write as a line equation, x=AOS

Function

Each x has only 1 y

Max/min

Highest or lowest point on the graph-the vertex

Completing the square

Note: a must be equal to 1 and you cannot divide into a radical

Vertex

Plug the value you get for axis of symmetry back into the formula as x, and the number you get will be the y term of the vertex. The x term of the vertex is the AOS number.

Solutions to quadratic equations

Roots, zeros (where the parabola crosses the x-axis)

The discriminant

The discriminant determines the number of real number solutions. Positive=2 0= 1 Negative= 0

Quadratic formula

The discriminant is everything under the square root symbol.

Y-intercept

(0,C) or plug 0 in as x

Number of solutions to quadratic function graphs

- 2 real solutions - 1 real solution (vertex is on origin) -0 real solutions, 2 imaginary (parabola does not cross the x axis)

Ways to solve quadratic equations

1. Factoring 2. Taking square roots 3. Quadratic formula 4. Completing the square

Taking square roots

Use only when there is no b term.