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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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data table
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

slide4

A Piecewise function

  • -0.00065x²+44.2832x-748117.4624, 32921 < x < 34064
  • f(x)=

0.00012x²-9.27624x+186518.9761, 38651< x < 41334

vertex form

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

standard form

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.

maximum minimum

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)

y intercept

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

quadratic formula

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)

slide10

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
slide11

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.
slide12

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.
slide13

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

standard form1

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.

maximum minimum1

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)

y intercept1

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

quadratic formula1

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)

slide18

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
slide19

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.
slide20

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.
5 years later
5 Years Later…..

y=1304x-2577568

*The average income and the medical care cost are predict to continue to rise.*

5 years later1
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