Explorations with a where y = ax² + 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.