Create an Equation of a Real-World Polynomial Shape
Many objects in the real world can be modeled as polynomials
functions. In this exercise, you will find a picture of an
object that takes the shape of at least a third-degree polynomial
(at least two humps). Place the object on a Cartesian
plane (x-y graph) and find the mathematical equation that models
the object.
Create An Equation Of A Real World Polynomial Shape Many Objects In The Real World Can Be Modeled As Polynomials Functio 1 (485.75 KiB) Viewed 314 times
Use the following example as a guide to create your own and unique polynomial function. 10 The roller coaster crosses the x-axis at four points. These are the roots of the function or where the function equal zero. We can write the roots as (x-(-9)), (x-(-1)), (x-3), and (x-8). So our polynomial can be written as: a-(x-(-9))-(x-(-1))-(x-3)-(x-8)= 0 or a-(x+9).(x+1)-(x-3)-(x-8) = 0 At this point we still need to calculate a. Another piece of information we can get from the graph is that the curve (roller coaster) crosses the y-axis at the point (-1). This means when x=0 we have y=-1 or f(0) = -1. a-(0+9) (0+1)-(0-3)-(0-8)= -1 a (9)-(1)-(-3)-(-8)= -1 a-216 = -1 a = -1/216 Therefore our polynomial function is: (x + 9).(x + 1)(x-3) (x-8) = 0 or 1 216 (x4x377x² - 195x+216) Quick check: From the graph it appears that when x=-5 then we have y = 8 (or close to 8). or Plugging x = -5 into our equation gives us: 1 ((-5)4 (-5)³77(-5)² - 195(-5)+216) = 8.12 216 1 216 f(-5) = 8.
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