Find a, b and c in f(x) = ax2+bx+c in order to have f([1,3]) =[1,3]?

Question

tip: apply some ideas from the Chaos Book.

Answer 1

The trick is to substitute the given values of x into the function, set the ax^2+bx+c equal to the given y, and thereby generate enough equations to solve for your unknowns. In this case you have three unknowns, so to get a complete solution you'd need three equations, which means you're one piece of information shy of a uniquely answerable question.

As a simpler example of what I mean, consider he question: "find a and b in f(x)=ax+b if f(1)=3." This is the equation of a line in the xy plane, and you'd need two points to determine it completely. Your shape, a parabola, requires three.

That said, you can develop three equations and, solving for (say) a and b in terms of the parameter c, develop an infinitude of solutions to the problem as you've stated it.

Answer 2

a=0 b= 1 c = 0

Answer 3

DOES THAT WORK AS A HTML