This is a free lesson from our course in Algebra II
In this lesson you will learn how to graph quadratic equations. When you explore it with the help of
some examples, audio and video presentation by the instructor in own hand writing,
it will be easy to understand. Remember that the graph of each quadratic is a curved
line called parabola.Parabolas always have a lowest point (or a highest
point, if the parabola is upsidedown). This point, where the parabola changes direction,
is called the "vertex".
One of the ways to start on graphing quadratics is by using intercepts. Once the possible intercepts have been graphed,
you may take help from table of values to finish up the graph. It helps you to find
the vertex, maximum and minimum values and the roots of a given equation. (More
text below video...)
(Continued from above) The general
rule for graphing is for equation ax^{2} + bx + c = 0,
if a is positive, then the parabola is axis up, vertex (0, 0), directrics is x = a, and foci (a
, 0). If a is negative then, the parabola is axis down, vertex (0, 0),
directrics is x = +a, and foci (a , 0). Further it explains
about the axis of symmetry, which is an imaginary line when drawn
the parabola is split into mirror image. Axis of symmetry is given by x
= 2b/a. The maximum or minimum value of the parabola is the y
value of the vertex. If a<0 ,it is minimum and if a>0 ,it
is maximum. The roots are the point of intersection of the parabola at the x axis. To
find the roots, set the quadratic equation equal to zero, factor it and solve it.
E.g. (5, 0) and (7, 0) are the roots of the parabola y = x^{
2} + 12x + 35.
In summary, the steps to graph quadratic equation are find the axis of symmetry,
find vertex, find roots, calculate two other points that lie on the parabola, plot
the points on parabola, draw and label the axis of symmetry, vertex and roots on
the graph.
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