1. Medical Care Cost vs. Average Income By: Larissa Ho

2. Data Table YearAverage Income ($)Medical Care Cost Per Year ($) 2001329215241 2002332525687 2003340646114 2004356486488 2005369526868 2006386517251 2007404057628 2008413347911 2009407118149 2010416738402 (2012). Health Care Costs: A Primer. In Kaiser Family Foundation. Retrieved from http://www.kff.org (2012). National Average Way Index Social Security. Retrieved from http://www.ssa.gov

3. Graph

4. A Piecewise function f(x)= -0.00065x²+44.2832x-748117.4624, 32921 < x < 34064 0.00012x²-9.27624x+186518.9761, 38651< x < 41334

5. Vertex Form Vertex: (34064, 6114) Point: (33252,5687) f(x)=a(x-34064)²+6114 5687=a(33252-34964) ²+6114 5687=a(-812) ²+6114 5687=a(659344)+6114 -6114 -427=a(659344) a= -0.00065 f(x)= -0.00065(x-34064) ²+6114 Leading Coefficient X coordinate of vertex Y coordinate of vertex Parabola A

6. f(x)= -0.00065(x-34064) ²+6114 = -0.00065(x-34064)(x-34064)+6114 = -0.00065(x²-34064x-34064x+1160356096)+6114 = -0.00065(x²-68128x+1160356096)+6114 = (-0.00065x²+44.2832x-754231.4624)+6114 f(x)= -0.00065x²+44.2832x-748117.4624 Standard Form Concave Up or Down? This parabola concaves down because in the standard and vertex form of the parabola, the leading coefficient (a) is negative. Parabola A

7. Maximum: (34064,6114) Maximum/Minimum Axis of Symmetry Coordinate of Vertex f(x)= -0.00065x²+44.2832x-748117.4624 y= -0.00065(34064)²+44.2832(34064)-748117.4624 y= -754231.4624+1508462.925-748117.4624 y= -754231.4624-748117.4624 y= 611.0002 Coordinate of Vertex: (34064, 6114) Parabola A

8. f(x)= -0.00065x²+44.2832x-748117.4624 f(x)= -0.00065(0)²+44.2832(0)-748117.4624 Y-intercept= -748117.4624 Y-Intercept X-Intercept Parabola A

9. f(x)= -0.00065x²+44.2832x-748117.4624 -0.00065x²: Quadratic 44.2832x: Linear 748117.4624: Constant Quadratic Formula Parts of the Equation This parabola cannot be factored because there is a leading coefficient, three terms, and the numbers are a large value. Grouping/FOIL Solutions from Quadratic Formula: 37140.9 and 30987.1 (Refer to previous slide) Parabola A

10. Number of Solutions There are two solutions. Real or Imaginary? Why? The solutions are real because when doing the quadratic formula there wasn’t a negative square root. This means the parabola never crosses through the x-axis. Check Work Point: (32921, 5241) 5241= -00065(32921)²+44.2832(32921)-748117.4624 5241= -704464.9567+1457847.227-78117.4624 5241= 753382.2703-748117.4624 5241=5264 Parabola A

11. f(x)=2(x-34064)²+6114 f(x)= -0.00065(x-34064)²+6114f(x)= 2(x-34064)²+6114 What Does This Mean in the Real World? It started out with a very low income, but a very high price for medical care which made it difficult for people to get the services. Then as time passed on, the income started to increase, and medical cost started to decrease which is good because then the services are affordable. However, income does continue to increase over time, but the price for medical care services increased. Parabola A

12. f(x)= -3(x-34064)²+6114 f(x)= -0.00065(x-34064)²+6114 f(x)= -3(x-34064)²+6114 What Does This Mean in the Real World? The income is increasing which is good because then people are able to purchase and pay for services. Additionally, the price for medical care decreased into the negatives which means the services are being provided without a cost. This is very unlikely to happen because the U.S economy relies on health care a lot. Therefore, it would be strange if these services are for free. Parabola A

13. Parabola B Vertex: (38651, 7251) Point: (40405, 7628) f(x)= a(x-38651)²+7251 7628= a(40405-38651)²+7251 7628= a(1754)²+7251 7628= a(3076516)+7251 377= a(3076516) a= 0.00012 f(x)=0.00012(x-38651)²+7251 Leading Coefficient X coordinate of vertex Y coordinate of vertex Vertex Form

14. Standard Form f(x)=0.00012(x-38651)²+7251 f(x)=0.00012(x-38651)(x-38651)+7251 f(x)=0.00012(x²-38651x-38651x+149389980)1+7251 f(x)=0.00012(x²-77302x+1493899801)+7251 f(x)=(0.00012x²-9.27624x+179267.9761)+7251 f(x)=0.00012x²-9.27624x+186518.9761 Concave Up or Down? This parabola concaves up because in the standard and vertex form of the parabola, the leading coefficient (a) is positive. Parabola B

15. Minimum: (38651, 7251) Maximum/Minimum Axis of Symmetry Coordinate of Vertex y =0.00012x²-9.27624x+186518.9761 y =179267.9761-358535.9522+186518.9761 y = 7251 Coordinate of Vertex: (38651, 7251) Parabola B

16. y =0.00012x²-9.27624x+186518.9761 y=0.00023(0)²-9.27624(0)+186518.9761 y=186518.9761 Y-Intercept X-Intercept Parabola B

17. f(x) = 0.00012x²-9.27624x+186518.9761 0.00012x²: Quadratic 9.27624x: Linear 186518.9761: Constant Quadratic Formula Parts of the Equation This parabola cannot be factored because there is a leading coefficient, three terms, and the numbers are a large value. Grouping/FOIL Parabola B (Refer to Previous Slide)

18. Number of Solutions None because it never hits the x-axis. Real or Imaginary? Why? The solutions are imaginary because when doing the quadratic formula there was a negative square root. This means the parabola will never cross the x- axis. Check Work Parabola B Point: (8149, 40711) y =0.00012x²-9.27624x+186518.9761 8149=0.00012(40611)²-9.27624+186518.9761 8149=198886.2625-377645.0066+186518.9761 8149=178758.7441+186518.9761 8149=7760.232

19. f(x)=2(x-34064)²+6114 What Does This Mean in the Real World? The people have negative incomes which is not possible in this situation, but it later increases over the time. It first starts off with medical services at a very high cost, but then it starts to decrease again. Additionally, after it decreases it starts to increase again. Parabola B f(x)=0.00012(x-38651)²+7251 f(x)=2(x-38651)²+7251

20. f(x)= -3(x-34064)²+6114 What Does This Mean in the Real World? The average income of a person is increasing year after year. Additionally, the price of medical services is negative which basically mean it’s free. This is not possible in this situation because the economy depends a lot of medical care, so it would be strange if these services are free. Parabola B f(x)=0.00012(x-38651)²+7251f(x)= -3(x-38651)²+7251

21. 5 Years Later….. y=1304x-2577568 *The average income and the medical care cost are predict to continue to rise.*

22. 5 Years Later….. Sample Calculation: y=1304x-2577568 y=1304(2011)-2577568 y=44776 Medical Care Cost 201144776 201246080 201347384 201448688 201549992 Average Income 20119148 20129528 20139908 201410288 201510668 Sample Calculation: y=380x-755032 y=380(2011)-755032 y=9148