Quadratic functions

A function is quadratic if it has this algebraic expression: y = f(x) = ax² + bx + c (a,b,c € R, a≠0), with a polynomial of degree 2.

Its graph is a parabola, with a relative extremum in a point called vertex of the parabola.

The vertex has x = -b/2a as abscissa, and the parabola has a symmetry axis in x = -b/2a.

To draw the graph, we calculate the vertex, the intersection points with axis and two or three points near the vertex.
Example:
    f(x) = x² -3x + 2

You can see the translations of the parabola and what happens with the sign of a in these examples:

Exercise: draw the graph of these functions:

a) f(x) = x² + 2x -3 = 0

b)

 

 

 

 

 

 

Solutions:

a) 

b)