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:
-
- Does the graph have a maximum point or a minimum point?
-The graph would be more to the left
-Minimum
-
- 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