The Shape of Quadratic Function

All the graph of quadratic function  y = ax^2 + bx + c have the same general shape, which is called a parabola. These parabola have a vertical axis of symetry. The point where a parabola meets its axis of simetry is called the vertex.

If  the value of a is positive then the vertex is at the lowest point (minimum value) of the graph.  If  the value of a is negative then the vertex is at the highest point (maximum value) of the graph. 

The larger size of  |a| the more the graph of quadratic function y = ax^2 + bx + c is elongated, that is, lengthened in the y –  direction.

Changing  the value of  b moves the axis of symetry of the graph of quadratic function y = ax^2 + bx + c in the  x – direction.

If  a and  b have the same sign then the axis of symetry is to the left of   y –  axis. If  a and  b have opposite signs then the axis of symetry is to the right of    the y – axis.Changing  the value of c moves the graph of quadratic function y = ax^2 + bx + c  up and down in the y – direction.

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