Finding Roots with the Bisection Method

Idea: Start with points xleft and xright with different signs (so there is a root between them!).
Take the midpoint and choose which half of the interval to keep using the sign at the midpoint.

Specifically: Start with xleft and xright where f(xleft) and f(xright) have different signs.
Set xnew = (xleft + xright)/2
if sign(f(xleft)) == sign(f(xnew))
	xleft = xnew;
else
	xright = xnew;
end

Repeat this until the estimated error is below epsilon (our desired accuracy of the solution)
We halve the error at each iteration, since our interval shrinks by a factor of 1/2.
This means the method has a linear convergence rate!

Look over bisection function
Note: sign(val) is 1 if val > 0, 0 if val == 0, -1 if val < 0
error function - displays provided message (in red) and stops execution

Example: Apply bisection method to f(x) = 6 - 2x^2
Know the roots are at +/-sqrt(3), just for example
Plot to find a starting interval

Set up and run bisection
Takes quite a few iterations, but finds a good approximation