Assignment #2 ~ Make it as Skinny or as Wide as You Want!
Manipulating Coefficient, a, of the Quadratic Equation
By Kevin Mylod
The graph of
the quadratic equation,
,
takes on the
shape of a parabola. The value of the coefficient, a, will
determine how narrow or wide the "inside" of the parabola
will be. Likewise, the value of a determines whether or
not the parabola opens up (holds water) or down (pours water).
If a takes on a positive value, then the parabola opens
up. Negative values of a will cause the parabola to open
down. Our first graph illustrates quadratic equations that have
a positive integer value for a.
The second graph
shows what happens to the parabola when the coefficient, a,
is a negative integer.
Finally, when
a takes on the value of other real numbers, such as fractions,
it will, again, effect the shape of the parabola. The smaller
the real number (i.e. the smaller the fraction), the wider the
parabola gets. In fact, as a approaches zero, the closer
the parabola gets to the x-axis, in which case the parabola
becomes the line, y = 0. The same holds true for negative
real number values as does negative integer values for a.
In an effort to keep redundancy to a minimum, its graph is left
for your own discovery.
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