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
  3. when


  4. Parity, odd parity
  5. if the function is neither even nor odd

    in — steamroom

  6. Continuity and differentiability
  7. A quadratic function is continuous and diferencian on the entire number line

  8. The increase and decrease, extrema
  9. if is decreasing on and increasing on , — minimum, — low

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

  10. The graph of a quadratic function is always a parabolawhose branches are directed upwards when and down when
  11. Coordinates of the vertex of the parabola:

    ; where

    The axis of symmetry of a parabola

Graphs of quadratic functions

Квадратична функція

Symmetry relative to the axis

Квадратична функція

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

Квадратична функція

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

Квадратична функція

Квадратична функція

The parabola crosses the axis at the point C

Квадратична функція

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
  4. 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
  3. (along the axis on , axis on )

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