Quadratic function, graph quadratic functions

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

Properties of quadratic functions

1. Scope



2. Multiple value

when

when

3. Parity, odd parity

if the function is neither even nor odd

in — steamroom

4. Continuity and differentiability

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

5. The increase and decrease, extrema

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

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

6. The graph of a quadratic function is always a parabolawhose branches are directed upwards when and down when

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

1. To calculate abscissa tops



2. Substitute into the equation and calculate the y coordinate of the top —
3. To build a sketch of the parabola ( ) vertex at point

when the branches up, with the branches down

II method

1. Razvesti quadratic equation
2. Using the elementary transformations of graphs, to perform a parallel transfer of a parabola

(along the axis on , axis on )