What are the important features of the graphs of quadratic functions?

1 Answer
Dec 16, 2014

A quadratic function has the general form:

(where #a,b and c# are real numbers) and is represented graphically by a curve called PARABOLA that has a shape of a downwards or upwards U.
The main features of this curve are:
1) Concavity: up or down. This depends upon the sign of the real number #a#:
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2) Vertex. The vertex is the highes or lowest point of the parábola.
the coordinates of this point are:
#x=-b/(2a)# and #y=-Delta/(4a)#
Where #Delta=b^2-4ac#

3) point of intercept with the y axis. This is the point where the parábola crosses the y axis and has coordinates: #(0,c)#

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4) Possible points of intercept with the x axis (there also can be none). These are the points where the parábola crosses the x axis.
They are obtained by putting y=0 and solving for x the 2nd degree equation: #ax^2+bx+c=0#, which will give the x coordinates of these points (2 solutions)
Depending on the discriminant #Delta=b^2-4ac# if it is <0 the parábola does not cross the x axis.
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