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

 

 

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