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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