Quadratic functions are usually the first we encounter that have curved or nonlinear graphs. The graph of a quadratic function is a specific kind of curve called a parabola (all parabolas are symmetric with respect to a line called the axis of symmetry). In algebra, quadratic functions are any form of the equation f(x) = ax^2 + bx + c, where a is not equal to 0.

The vertex of a parabola is the point at the bottom of the "U" shape (or the top, if the parabola opens downward). The equation for a parabola can also be written in "vertex form": f(x)=a(x−h)^2+k. In this equation, the vertex of the parabola is the point (h,k).

Created with GeoGebra by Vitor Nunes

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There are two "families" of quadratic functions. Try changing the parameters of each of the functions.

Let f be the functions of type:
a(x-h)^2 + k

Let g be the functions of type:
ax^2 + bx + c