# Victor L. Brunaud-Vega

After exploring all of Assignment 2, I selected some for this Write-up.

1. Construct graphs for the parabola  y=ax2+bx+c  for different values of a, b, and c. (a, b, c can be any rational numbers).

a)   Trying different values for a.

Keeping b=1 and c=1, I tried different values for a.  It gave me a parabola crossing the y axis at (0,1) and, if the value of a=0, then the line becomes straight and crossing the x axis at point

(-1,0).   If the value of a is negative, then the parabola opens downwards.  If the value of a is positive, then the parabola opens upwards.

Here is an animation showing the behavior of the line as the value of a changes.

b)   Trying different values for b.

Keeping a=1 and c=1, now I tried different values for b.  The result was a parabola moving through all the four quadrants but crossing the y axis only at the point (0,1).  It looks like b controls the location of the axis of symmetry.

Here is an animation to watch the effect of changing the value of b.

c)   Trying different values for c,

Keeping a=1 and b=1, it is time to try different values for c.  Now the result was a parabola going up and down, crossing the y axis in several points.

The parabola crosses the origin of the system (0,0) when c=0.  And, if c = 1, then the parabola crosses the y axis at point (0,1).  It looks like c controls the point where the parabola crosses the y axis.

Here is an animation to watch the effect of changing the value of c.

d) Trying different values for a and b.

What happens if we change the values of two parameters?  Changing a and b we know that the parabola will cross the y axis only at the point (0,1) because that is the parameter represented with c.

Apparently, the parameter c controls the point where the parabola crosses the y axis and b controls the location of the axis of symmetry.

In the pictures below there are graphics for different values of a, b, and c respectively.