1. By: Denis Alekhin

2. f(x)=ax 2 +bx+c f(x)=a(x-h) 2 +k Quadratic Constant Linear Determine which way the graph goes and how steep Moves the vertex up or down Moves the vertex left or right

3.  Points: Point 1 (34064,6114), Point 2 (33252,5687), Point 3 (32921,5241)  Equations: Vertex form: f(x)=-0.00065(x-34064) 2 +6114 General form: f(x)=-0.00065x 2 +44.2832x- 748117.4624

4. Graph

5. Piecewise Function: f(x)={32921<x<34064 36952<x<40711} Graph

6.  Real solutions are when the parabola crosses the x axis and imaginary solutions are when the parabola does not cross the x axis.  My problem has 2 real solutions because the parabola costs the x axis 2 times.

7.  To fins axis of symmetry, you use the equation –b/2a to solve for.  Example: -b/2a -(44.2832)/2(-0.00065) -44.2832/-0.0013 34064 Axis of Symmetry is 24064 My Equation: f(x)=-0.00065x 2 +44.2832x- 748117.4624

8.  The vertex is where the maximum or the minimum of the parabola.  The vertex of my problem is: (34,064,6114)  The x intercepts is when the parabola crosses the x axis and y intercepts is when the parabola crosses the y axis.  X and Y intercepts in my problem: y intercept = -748117.4624 x intercept = 30997.05464 and 37130.94536

9. This is the quadratic formula. Example: -(44.2832)±√(44.2832) 2 -4(-0.00065) (748117.4624)/ 2(-0.00065) -44.2832±√15.896/-0.0013 30997.05464 and 37130.94536 My Equation: f(x)=-0.00065x 2 +44.2832x- 748117.4624

10.  I use the equation I got and plug a point in the x and y.  Example: Point I use: (32921,5241) f(x)=-0.00065x 2 +44.2832x-748117.4624 5241=-0.00065(32921) 2 +44.2832(32921)- 748117.4624 5241=5241 The equation works.

11. The effect would be the parabola flipping my data making the actual parabola open up opposed to opening down. In real world the prices would start out high and then become cheaper and then rise again to higher price. This could happen by having a bad economy and then the economy got good and people start to buy insurance and then it rose again so the economy went bad again.

12. The effect would be that medical went down so low that they became free to people. The number can be negative because it does not make sense to have negative money. This could happen by having the government paying for your health care.