Power functions > Quadratic functions
12345Quadratic functions

Theory

Take a look at the applet: Quadratic Functions

A function of the form f ( x ) = a ( x p ) 2 + q , is called a quadratic function (if a 0 ).
The graph of a quadratic function can be derived by transformations of the graph of y = x 2 .
The graph of every quadratic function is a parabola with vertex ( p , q ) andaxis of symmetry x = p .
If a > 0 then the parabola will open upwards.
If a < 0 then the parabola will open downwards.

The quadratic equation a ( x p ) 2 + q = u can be rewritten as: ( x p ) 2 = c .

  • If c > 0 there are two solutions.

  • If c = 0 there is only one solution.

  • If c < 0 there are no solutions.

You can find the solutions by using radicals.

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