Look at the graph of the parabola: y = ax2 + bx + c
Now look at various values for a in the equation, letting b and c both equal 1:
We see that changing the value of a changes the shape of our parabola.
Various observations can be made about the graph in relation to a changing a:
· If a is positive, the graph faces up. If a is negative, the graph faces downward.
· When a is small, the parabola is quite fat. The larger a gets, the skinnier the parabola becomes.
Take a look at the animation of changing a in Graphing Calculator: click here
(note: you must have Graphing Calculator to see this function)
Now varying values of b, while a and c equal 1:
Changing the values of b moves our vertex.
A negative b moves the curve to the right. A positive b moves the curve to the left.
Take a look at the animation of changing b in Graphing Calculator: click here
Now as c changes, how the graph changes, variables a and b both equal 1…
Changing c moves the parabola up or down.
A negative c moves the curve down. A positive c moves the curve up on the axis.
Take a look at the animation of changing c in Graphing Calculator: click here