Solve application problems using quadratic functions.

Question

A person’s systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person’s age, in years. The equation: P = 0.004y² - 0.02y + 120 gives a person’s blood pressure, P, at age y years.

A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 45 years.

B.) If a person’s systolic pressure is 127.54 mm Hg, what is their age (rounded to the nearest whole year)?

Answer 1

To find the systolic pressure for a person of age 45 years, just plug in y = 45:

P = 0.004y² - 0.02y + 120

P = 0.004(45)² - 0.02(45) + 120

P = 0.004(2025) - 0.9 + 120

P = 8.1 - 0.9 + 120

P = 127.2

To find a person's age if their systolic pressure is 127.54 mm Hg, plug in P = 127.54

P = 0.004y² - 0.02y + 120

127.54 = 0.004y² - 0.02y + 120

0 = 0.004y² - 0.02y - 7.54

Use the quadratic formula to solve this. The quadratic formula (for ay² + by + c = 0) is:

y = [-b ± √(b² - 4ac)]/(2a)

In this case a = 0.004, b = - 0.02 and c = - 7.54 so:

y = [-b ± √(b² - 4ac)]/(2a)

y = [-(-0.02) ± √((0.02)² - 4(0.004)(-7.54))]/(2(0.004))

y = [0.02 ± √(0.0004 + 0.12064)]/0.008

y = [0.02 ± √0.12104]/0.008

y = [0.02 ± 0.3479]/0.008

So, breaking it into 2 parts

1) y = [0.02 + 0.3479]/0.008 or y = 0.3679/0.008 = 45.989

2) y = [0.02 - 0.3479]/0.008 or y = -0.3279/0.008 = -40.989

Since -40.988 makes no sense (40.989 years before birth), we throw that answer out.

The age where a person's systolic pressure is 127.54 mm Hg is 46 (rounded)

Answer 2

Question: A person’s systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person’s age, in years. The equation: P = 0.004y² - 0.02y + 120 gives a person’s blood pressure, P, at age y years.

A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 45 years.

B.) If a person’s systolic pressure is 127.54 mm Hg, what is their age (rounded to the nearest whole year)?

Answer: Sounds like bloody good fun!

Your model is a parabola that opens upwards, so let's identify this trend: as age increases, so will systolic blood pressure. You should be able to discard values of y (age in years) that are less than zero, since it is not possible to have a negative age.

A.) You're given the age, and asked to find the systolic pressure. Plug in 45 where you see "y":

P = 0.004(45)² - 0.02(45) + 120 = 127.2 mm Hg.

B.) This is where the problem will look more like your quadratic formula process. Plug in 127.54 for P, and solve for y.

(127.54) = 0.004y² - 0.02y + 120 ---> 0 = 0.004y² - 0.02y - 7.54. This is in the standard form of a quadratic equation.

Identify a, b, and c here. a = 0.004, b = -0.02, c = -7.54. Place these numbers into the quadratic formula and simplify. Round to the nearest whole year. Although you'll get two answers, keep the positive answer since negative years do not make sense in this real world application.

y is approximately 45.988504, and upon rounding, we find that a person who is 46 years of age will have a systolic blood pressure of 127.54 mm Hg.