Medical Care Cost vs. Average Income By: Larissa Ho

Data TableYear Average Income

($)Medical Care Cost

Per Year ($)2001 32921 52412002 33252 56872003 34064 61142004 35648 64882005 36952 68682006 38651 72512007 40405 76282008 41334 79112009 40711 81492010 41673 8402

(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

32921 34921 36921 38921 40921 429210100020003000400050006000700080009000

Average Income vs. Medical Care Cost

Average Income ($)

Med

ical

Car

e Co

st P

er Y

ear

($)

A Piecewise function

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

Vertex Form Vertex: (34064, 6114) Point: (33252,5687)f(x)=a(x-34064)²+61145687=a(33252-34964) ²+61145687=a(-812) ²+61145687=a(659344)+6114-6114 -6114-427=a(659344)a= -0.00065f(x)= -0.00065(x-34064) ²+6114

Leading Coefficient

X coordinate of vertex

Y coordinate of vertex

Parabola A

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)+6114f(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

Maximum: (34064,6114)Maximum/Minimum

Axis of Symmetry

Coordinate of Vertex f(x)= -0.00065x²+44.2832x-748117.4624y= -0.00065(34064)²+44.2832(34064)-748117.4624y= -754231.4624+1508462.925-748117.4624y= -754231.4624-748117.4624y= 611.0002Coordinate of Vertex: (34064, 6114)

Parabola A

f(x)= -0.00065x²+44.2832x-748117.4624f(x)= -0.00065(0)²+44.2832(0)-748117.4624Y-intercept= -748117.4624

Y-Intercept

X-Intercept

Parabola A

f(x)= -0.00065x²+44.2832x-748117.4624-0.00065x²: Quadratic44.2832x: Linear748117.4624: 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

Number of SolutionsThere 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 WorkPoint: (32921, 5241)5241= -00065(32921)²+44.2832(32921)-748117.46245241= -704464.9567+1457847.227-78117.46245241= 753382.2703-748117.46245241=5264

Parabola A

f(x)=2(x-34064)²+6114

f(x)= -0.00065(x-34064)²+6114

f(x)= 2(x-34064)²+6114What 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

f(x)= -3(x-34064)²+6114

f(x)= -0.00065(x-34064)²+6114

f(x)= -3(x-34064)²+6114What 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

Parabola B

Vertex: (38651, 7251) Point: (40405, 7628)f(x)= a(x-38651)²+72517628= a(40405-38651)²+72517628= a(1754)²+72517628= a(3076516)+7251377= a(3076516)a= 0.00012f(x)=0.00012(x-38651)²+7251

Leading Coefficient

X coordinate of vertex

Y coordinate of vertex

Vertex Form

Standard Form f(x)=0.00012(x-38651)²+7251f(x)=0.00012(x-38651)(x-38651)+7251f(x)=0.00012(x²-38651x-

38651x+149389980)1+7251f(x)=0.00012(x²-77302x+1493899801)+7251f(x)=(0.00012x²-9.27624x+179267.9761)+7251f(x)=0.00012x²-9.27624x+186518.9761Concave 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

Minimum: (38651, 7251)Maximum/Minimum

Axis of Symmetry

Coordinate of Vertex y =0.00012x²-9.27624x+186518.9761y =179267.9761-358535.9522+186518.9761y = 7251

Coordinate of Vertex: (38651, 7251)

Parabola B

y =0.00012x²-9.27624x+186518.9761y=0.00023(0)²-9.27624(0)+186518.9761y=186518.9761

Y-Intercept

X-Intercept

Parabola B

f(x) = 0.00012x²-9.27624x+186518.97610.00012x²: Quadratic9.27624x: Linear186518.9761: 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)

Number of SolutionsNone 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+186518.97618149=0.00012(40611)²-9.27624+186518.97618149=198886.2625-377645.0066+186518.97618149=178758.7441+186518.97618149=7760.232

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

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+7251

f(x)= -3(x-38651)²+7251

5 Years Later…..

2000

2002

2004

2006

2008

2010

2012

05000

1000015000200002500030000350004000045000

Medical Care Cost and Average Income Over Time

Medical Care Cost Average Income

Year

Mon

ey ($

)

y=380x-755032

y=1304x-2577568

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

5 Years Later…..

Sample Calculation:y=1304x-2577568y=1304(2011)-2577568y=44776

Medical Care Cost 2011 447762012 460802013 473842014 486882015 49992

Average Income2011 91482012 95282013 99082014 102882015 10668Sample Calculation:y=380x-755032y=380(2011)-755032y=9148