Project 17: Finding X-Intercepts
Suppose we want to find the dimensions of a particular cube that has the following properties:
The length is unknown, so we will call it X.
The width is 3 more than the length (X + 3)
The height is 2 less than the length (X - 2)
The volume of the cube is 200 sq. inches.
V = X(X +3)(X-2) = x^3 + x^2 - 6x
x^3 + x^2 - 6x = 200
To solve this equation, we can write the equation as x^3 + x^2 - 6x - 200 = 0
Now, if we can find the x-intercept of the equation (where x is positive) we find that X = 5.856
So the length is 5.856, the width is 8.856, and the height is 3.856.
Some more examples of finding x-intercepts are shown below:
For the polynomial above, there is one zero (x-intercept) between the values x = -1 and x = 3. The zero is x = 1.
For the polynomial above, there are two zeros (x-intercepts) between the values x = -4 and x = -1. The zeros are x = -3 and x = -1.
For the polynomial above, there are no zeros (x-intercepts) between the values x = -1 and x = 0.
Project 17:
The following variables have been initialized 'lowerX', 'upperX', 'co'. There is also a working method called getYPoly.
lowerX is the lower bound for the range in which you are searching for an x-intercept. For the first example above, lowerX is -1.
upperX is the upper bound for the range in which you are searching for an x-intercept. For the first example above, upperX is 3.
co is an array of values that represent the polynomial's coefficients in ascending order
example: if a polynomial is y = x^3 - 4x^2 - 11x + 30
The array 'co' would hold values: {30, -11, -4, 1}.
getYPoly is a method that accepts an array of coefficients (representing the coefficients of a polynomial) and an x-value. The method returns the y-value for the polynomial at the given x.
Example: If 'co' holds the coefficients for the polynomial graphed above, getYPoly(co, 0.0) would return -6.0.
Task:
Appropriately assign the value of 'zero'.
'zero' should not have a value if there are no x-intercepts between x = lowerX and x = upperX.
'zero' should be assigned to an intercept between x = lowerX and x = upperX if at least one exists.
For the Polynomial shown below (coefficients would be: 0,5,-5,1), and lowerX = 1.0 and upperX = 3.0, zero would be a number close to 1.38.
**If your code works for 5 test cases in a row, you can enter your e-mail address.
Universal Computational Math Methods:
pow(5,2) returns 25.0
abs(-3.0) returns 3
sqrt(49.0) returns 7.0