# Assignment 2: Quadratics

## Varying Coefficients

### Here's a graph of a
quadratic equation

###

###

## What happens if we adjust the
term?

###

The following graph the
adds the quadratic equation

:

#### Blue: ,
Purple:

###

### What changed from
to
?

How did that change affect the graph?

###

### The general form of
the equations shown above is

### We can have all sorts of combinations
of __a__, __b__, & __c__:

###

### The graph below shows
various values for __a__, where __b__ = 1
and __c__ = 1;

That is, __a__ changes while __b__ and __c__
are both fixed.

{Note: In each of these cases, __a__ is a POSITIVE value}

#### Values for `a`

Light Blue: 0.5; Purple: 1; Blue: 2; Red: 3

###

###

###

### How does changing the
coefficient `a` seem to affect the behavior of
the graph?

###

###

###

###

## What happens when __a__
is a Negative value?

###

###

### The equations graphed
below all have negative a values.

Is that what you expected?

###

### How does a negative
value for __a__ change the graph?

###

#### Values for `a`

Light Blue: -0.5; Purple: -1; Blue: -2; Red: -3

###

###

## What happens when __a__
= 0?

###

### Here is a graph that shows various
negative values of __a__ that get closer and closer
to zero.

### How are the graphs changing?

###

### Are you sure?

What if we zoom out some?

### How about if we zoom even further?

### More still?

###

### This graph shows values of a
getting closer and closer to zero from both the positive and negative
side.

### Let's zoom back in, this time.

### And again.

### As a goes to zero, what can you
say about the behavior of the quadratic equation

# Changing
*a*

###

###

### Can you characterize how changing
__a__ changes the graph?

###

# Changing
*b*

###

### What happens when we
adjust the b value?

### Remember, we are looking at the
general equation:

### The graph below shows various
positive values of __b__

#### Values for __b__

Purple: 1; Red: 2; Blue: 3; Green: 5; Light Blue - 7

### What do you think will
happen when we vary negative values of __b__?

###

###

###

### Can you characterize how changing
__b__ changes the graph?

###

# Changing
*c*

###

### What affect will adjusting
c, the "constant", have?

#### Values for __c__

Purple: 1; Red: 2; Blue: 3; Green: 5; Light Blue - 7

### What affect will negative
values of __c__ have on a graph?

####

###

### Can you characterize how changing
__c__ changes the graph?

###

### Ok. Take a look a the
graphs below. What can you determine about *a*, *b*,
& *c*?

What is changing? What causes the line with a negative slope?

###

###

### How about these? Can
you characterize *a*, *b*, & *c*?

###