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 parabolawhose 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
![Квадратична функція](http://cdn.cubens.com/contents/pictures/quadratic-function-1.png)
Symmetry relative to the axis
![Квадратична функція](http://cdn.cubens.com/contents/pictures/quadratic-function-2.png)
The graph of the function is stretched or stretched with
respect to the axis
by the number of units equal to the number and
![Квадратична функція](http://cdn.cubens.com/contents/pictures/quadratic-function-3.png)
![Квадратична функція](http://cdn.cubens.com/contents/pictures/quadratic-function-4.png)
The graph of the function rises at or falls with
the number of units equal to the number of c
![Квадратична функція](http://cdn.cubens.com/contents/pictures/quadratic-function-5.png)
![Квадратична функція](http://cdn.cubens.com/contents/pictures/quadratic-function-6.png)
The parabola crosses the axis at the point C
![Квадратична функція](http://cdn.cubens.com/contents/pictures/quadratic-function-7.png)
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
)