Assignment #2

Investigating the Graph of the Parabola

y = ax2 + bx + c

By

Michelle Nichols

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