**Definition:** a Quadratic function is called a function of the form where

## Properties of quadratic functions

- Scope
- Multiple value
- Parity, odd parity
- Continuity and differentiability
- The increase and decrease, extrema
- The graph of a quadratic function is always a
**parabola**whose branches are directed upwards when and down when

when

when

if the function is neither even nor odd

in — steamroom

A quadratic function is continuous and diferencian on the entire number line

if is decreasing on and increasing on , — minimum, — low

when increasing on and decreasing on , — high, — high

Coordinates of the vertex of the parabola:

; where

The axis of symmetry of a parabola

## Graphs of quadratic functions

*Symmetry relative to the axis*

*The graph of the function is stretched or stretched with respect to the axis by the number of units equal to the number and*

*The graph of the function rises at or falls with the number of units equal to the number of c*

*The parabola crosses the axis* *at the point C*

## How to graph quadratic functions

**And method**

- To calculate abscissa tops
- Substitute into the equation and calculate the y coordinate of the top —
- To build a sketch of the parabola ( ) vertex at point

when the branches up, with the branches down

**II method**

- Razvesti quadratic equation
- Using the elementary transformations of graphs,
**to perform a parallel transfer of a parabola**

(along the axis on , axis on )