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Medical Care Cost vs. Average Income

Medical Care Cost vs. Average Income . By: Larissa Ho . Data Table. (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. Graph. A Piecewise function.

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Medical Care Cost vs. Average Income

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

  2. Data Table (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 • -0.00065x²+44.2832x-748117.4624, 32921 < x < 34064 • f(x)= 0.00012x²-9.27624x+186518.9761, 38651< x < 41334

  5. Parabola A 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 -6114 -427=a(659344) a= -0.00065 f(x)= -0.00065(x-34064)²+6114 Y coordinate of vertex Leading Coefficient X coordinate of vertex

  6. Parabola A Standard Form 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 Concave Up or Down? This parabola concaves down because in the standard and vertex form of the parabola, the leading coefficient (a) is negative.

  7. Parabola A Maximum/Minimum Axis of Symmetry Maximum: (34064,6114) 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)

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

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

  10. Parabola A Number of Solutions Real or Imaginary? Why? There are two solutions. 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

  11. Parabola A • f(x)=2(x-34064)²+6114 • f(x)= -0.00065(x-34064)²+6114 • f(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.

  12. Parabola A • f(x)= -3(x-34064)²+6114 • f(x)= -3(x-34064)²+6114 • f(x)= -0.00065(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.

  13. Parabola B • Vertex Form 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 Y coordinate of vertex Leading Coefficient X coordinate of vertex

  14. Parabola B 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.

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

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

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

  18. Parabola B Number of Solutions Real or Imaginary? Why? None because it never hits the x-axis. 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 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. Parabola B • f(x)=2(x-34064)²+6114 • f(x)=2(x-38651)²+7251 • f(x)=0.00012(x-38651)²+7251 • 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.

  20. Parabola B • f(x)= -3(x-34064)²+6114 • f(x)=0.00012(x-38651)²+7251 • f(x)= -3(x-38651)²+7251 • 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.

  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 • Sample Calculation: • y=380x-755032 • y=380(2011)-755032 • y=9148

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