Graph of the function y = ax² + bx + c. Quadratic function (parabola)

General form of a quadratic function

A quadratic function is given by

y=ax^2+bx+c

with

a\neq0

. The coefficient

a

, as for

y=ax^2

, tells which way the branches open: up if

a>0

, down if

a<0

. The terms

bx

and the constant

c

shift the parabola in the plane: the vertex is usually no longer at

(0;0)

It is still the same parabola, only in a different position

The zeros of the function are the

x

-coordinates where the graph meets the

x

-axis

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