Messing around with math...

quadradic_solver.cpp

#include <cmath>
#include <iostream>

int main()
{
	double a, b, c;
	std::cout << "Quadratic formula solver.\nGive A:" << std::endl;
	std::cin >> a;
	std::cout << "Give B:" << std::endl;
	std::cin >> b;
	std::cout << "Give C:" << std::endl;
	std::cin >> c;
	
	double descriminant = (b * b) - (4 * a * c);
	if (descriminant < 0)
	{
		std::cout << "The answers are imaginary." << std::endl;
		
		double vertex_x = (-b) / (2 * a);
		double vertex_y = (a * (vertex_x * vertex_x)) + (b * vertex_x) + c;
		
		const char* direction =  (a>0) ? "upward." : "downward.";
		std::cout << "The direction is " << direction << std::endl;
		std::cout << "The vertex is (" << vertex_x << ", " << vertex_y << ")" << std::endl;
		std::cout << "The y-intercept is (0," << c << ")" << std::endl;
	}
	else if (descriminant == 0)
	{
		std::cout << "There is one real answer." << std::endl;

		double answer = (-b) / (2 * a);

        	const char* direction =  (a>0) ? "upward." : "downward.";
		std::cout << "The answer is: " << answer << std::endl;
		std::cout << "The direction is " << direction << std::endl;
		std::cout << "The vertex is (" << answer << ", 0)" << std::endl;
		std::cout << "The y-intercept is (0," << c << ")" << std::endl;
	}
	else
	{
		std::cout << "There are two real answers." << std::endl;

		double answer_a = (-b - sqrt(descriminant)) / (2 * a);
		double answer_b = (-b + sqrt(descriminant)) / (2 * a);
		
		double vertex_x = (-b) / (2 * a);
		double vertex_y = (a * (vertex_x * vertex_x)) + (b * vertex_x) + c;

        	const char* direction =  (a>0) ? "upward." : "downward.";
		std::cout << "The answers are: { " << answer_a << ", " << answer_b << "}" << std::endl;
		std::cout << "The direction is " << direction << std::endl;
		std::cout << "The vertex is (" << vertex_x << ", " << vertex_y << ")" << std::endl;
		std::cout << "The y-intercept is (0," << c << ")" << std::endl;
	}

	return 0;
}