Explorations with a where y = ax^{2} + bx +c

When a is manipulated within a range of values, keeping b and constant the
parabola expands, shifts, flips and will even straighten as shown below. The
line forms when we use zero for a as our equation
becomes linear. One might notice that our y intersect remains constant as our c
is held constant at 2. The extrema of our parabolas
shifts as our a changes demonstrating that extrema are dependent upon the a value.