To solve an equation by finding x-intercepts, Cynthia graphed the function y=x^3-5x+|2x-3|. Give several possibilities for the original equation.
Thanks
See
http://www.jiskha.com/display.cgi?id=1252206912
To find the x-intercepts of the given function, we need to set y equal to zero and solve for x.
The given function is y = x^3 - 5x + |2x - 3|.
Setting y = 0, we have 0 = x^3 - 5x + |2x - 3|.
To find the x-intercepts, we can split the equation into two cases, based on whether (2x - 3) is positive or negative:
Case 1: (2x - 3) is positive (greater than or equal to 0):
In this case, we have 0 = x^3 - 5x + (2x - 3).
Simplifying further, 0 = x^3 - 3x - 3.
We can solve this equation using different methods, such as using factoring, the rational root theorem, or numerical methods like the Newton-Raphson method.
Case 2: (2x - 3) is negative (less than 0):
In this case, we have 0 = x^3 - 5x - (2x - 3).
Simplifying further, 0 = x^3 - 7x + 3.
Again, we can solve this equation using different methods.
Overall, the original equation that Cynthia graphed could have been several possibilities based on the two cases above:
Case 1: x^3 - 3x - 3 = 0 (when (2x - 3) is positive)
Case 2: x^3 - 7x + 3 = 0 (when (2x - 3) is negative)
By solving these equations, you can find the x-intercepts of Cynthia's graph and determine all the possible original equations.