Exploring quadratic functions

1.)  Quadratic equation: A polynomial equation of the second; the standard form

of a quadratic equation ax^2+bx+c=0

2.)  Example of quadratic function: 2x^2+4x+3=0

Example of a function not quadratic: 1x^2 + 0 + 1

3.)The right side of the graph goes slightly out more than the left

 

4.) y= 4x^2 + 2x+ 2

 

y= 5x^2 + 3x + 3

 

The graphs both are more on the left side. y= 4x^2 + 2x+ 2 <—– This graph is under the 2 y axis, more to the left of the y axis and goes up outwards.

y= 5x^2 + 3x + 3 <—– This graph is on the 3 y axis and goes up outwards.

 

 

5.) Keep b and c constant (ie. Don’t change their value). Describe what happens to the graph when:

    1. Does the graph have a maximum point or a minimum point?

-The graph would be more to the left

-Minimum

 

    1. Does the graph have a maximum point or minimum point?

-the graph would be above the 0 X axis

-Maximum

-The graph is above the x axis slightly to the left of the Y axis spreading outwards

 

 

-The graph is more towards the left in the negative X region spreading out upwards

 

6.) When the graph is below 0 its a maximum and when the graph is above 0 it’s a minimum

 

7.)  When C changes the minimum goes up or down

 

 

Part 2:

See if by adjusting the sliders, you can get a curve that just touches the x axis (y=0).

 

Equation: y= 4x^2 + 0x + 0

 

Adjust the sliders so you can get the roots of 1 and -1

 

Equation: y = 0.1x^2 + 0x + 10   <—– 1 solution

 

 

Adjust the sliders so that the curve does NOT cross the x-axis.

 

Equation:  y = 2x^2 + 0 + 2 <—- 2 solutions