#include <stdio.h>
#include <math.h>
#include <string.h>

int main(void)  {
    char form[25];
    char var[10];
    int a, h, k;
    int vertex;
    int upDown = 0;
    int oldK, oldH = 0;
    float aTwo, b, c;
    char parabola[10];
    float five = 0.0;
    float y, x;

    printf("Hello, would you like to use vertex form or standard form? \n");
    scanf("%s", form);

    printf("\n --------------------------------- \n \n");

    if(strcmp(form, "vertex") == 0) {
        printf("Vertex form is Y = a(x-h)² + k \n");   //PEMDAS

        printf("\n --------------------------------- \n \n");

        printf("Do you have the variables a, h, and k? Answer Yes or No.\n");
        scanf("%s", var);

        printf("\n --------------------------------- \n \n");

        if(strcmp(var, "yes") == 0) {   //This program tells the user about the various things that their formula gives them
            printf("Please enter the variables in the following order: a, h, and then k \n");
            scanf("%d %d %d", &a, &h, &k);

            printf("\n --------------------------------- \n \n");

            //int oldKTwo = k;
            oldH = h;

            //Movement left and right
            if(h>0) {   //so if H is positive, continue
                //H will go right
                printf("The X goes right by %d \n", h);
            }
            else    {   //So the H is negative here
                //H will go left
                printf("The X goes left by %d \n", abs(h));
            }


            //Movement up and down
            if(k>0) {   //K is positive here
                //K goes up here
                printf("The Y will go up by %d \n", k);
            }
            else    {   //K is negative here
                //K will move down here
                printf("The Y will go down by %d \n", abs(k));
            }

            if(a>1) {
                printf("The parabola has been stretched by a factor of %d \n", a);
            }
            else    {
                printf("The parabola has been compressed by a factor of %d, and has been flipped across the X axis. \n", abs(a));
                upDown = 1;
            }

            //Axis of symmetry; X = H
            printf("The Axis of Symmetry is X = %d \n", h);

            //Max or Min; if upDown == 1, then it's opening down, and it will have a Max
            if(upDown == 1) {
                printf("The maximum is %d \n", k);
            }
            else    {
                printf("The minimum is %d \n", k);
            }

            //Domain & Range
            printf("The Domain is = all real numbers \n");
            if(upDown == 1) {
                printf("The Range is = all real numbers LESS than or EQUAL to %d \n", k);
            }
            else    {
                printf("The Range is = all real numbers GREATER than or EQUAL to %d \n", k);
            }


            //Vertex
            printf("Vertex is (%d, %d) \n", h, k);


            printf("\n --------------------------------- \n \n");


            if(h<0) {

                if(k<0) {
                    printf("Your vertex formula is Y = %d(x+%d)² - %d \n", a, abs(h), abs(k));
                }
                if(k>0) {
                    printf("Your vertex formula is Y = %d(x+%d)² + %d \n", a, abs(h), k);
                }

            }

            if(h>0) {

                if(k<0) {
                    printf("Your vertex formula is Y = %d(x-%d)² - %d \n", a, h, abs(k));
                }
                if(k>0) {
                    printf("Your vertex formula is Y = %d(x-%d)² + %d \n", a, h, k);
                }

            }

            printf("\n --------------------------------- \n \n");

            //Vertex to Standard form
            //(a+b)² = a² + 2ab + b²

            /*                          Example
                    Y = a(x-h)² + K    >>> Y = Ax² + Bx + C
                    (a+b)² = a² + 2ab + b²
                    (x-h)² = x² + 2x*(-h) + (-h)²    *

                    Y = 2(x+3)² - 22
                    (x+3)² = x² + 6x + 9
                    Y = 2(x² + 6x + 9) -22
                    Y = 2x² + 12x + 18 - 22
                    Y = 2x² + 12x - 4

                    Y = a(x-h)² + k
                    Y = a(x² + 2x(-h) + (-h)²) + k
                    Y = ax² + a*2x(-h) + a(-h)² + k
                    Then                            ^ combine ^
            */

            if(h<0) {

            //printf("Y = %d(x-(%d))² + (%d) \n", a, h, k);
            int kaiser = 2 * h;
            int schibbe = pow(h, 2);
            //printf("(x+(%d))² = x² + %dx + (%d) \n", h, abs(kaiser), schibbe);

            //printf("Y = %d(x² + %dx + (%d) + %d \n", a, abs(kaiser), schibbe, k);
            int lacht = a * schibbe;
            int rein = a * abs(kaiser);
            int kurwa = lacht + k;
            printf("Your standard formula is Y = %dx² + (%d)x + (%d) \n", a, rein, kurwa);
            }

            if(h>0) {
            int kaiser = 2 * h;
            int schibbe = pow(h, 2);

            int lacht = a * schibbe;
            int rein = a * abs(kaiser);
            int kurwa = lacht + k;
            printf("Your standard formula is Y = %dx² - (%d)x + (%d) \n", a, rein, kurwa);
            }

            /*printf("Y = %d(x-(%d))² + (%d) \n", a, h, k);
            int kaiser = 2 * h;
            int schibbe = pow(h, 2);
            printf("(x+(%d))² = x² + %dx + (%d) \n", h, kaiser, schibbe);
            printf("Y = %d(x² + 2x(%d) + (%d)²) + %d \n", a, h, h, k);
            printf("Y = %dx² + %d * 2x(%d) + %d(%d)² + %d \n", a, a, h, a, h, k);*/



            //printf("Your standard formula is Y = ")

        }

        /*if(strcmp(var, "no") == 0)    {   //This program will write the formula for the user based on the things they input
            printf("Please enter the following: \n");

            //Enter vertex
            printf("Vertex \n");
            scanf("%d %d", &h, &k);

            //Does it open up or down
            //printf("Does it open or down? \n");
            //scanf("%s", parabola);    //If up, the a will be positive. If down, the a will be negative

            //if the points move by something, you can find out what a is by putting Y/X and simplifying

            printf("What is another point? (x,y)\n");
            scanf("%d %d", &x, &y);

            printf("\n --------------------------------- \n \n");


            //printf("Your current two points are v(%d, %d) and (%d, %d) \n \n \n", h, k, x, y);

            float aa = y/x;

            printf("The formula is Y = %g(x - (%d)) + (%d) \n", aa, h, k);


            //Y = a(x-h)² + k
        }*/

    }

    if(strcmp(form, "standard") == 0)   {
        printf("Standard form is Y = Ax² + Bx + C \n \n");

        printf("Please enter the variables in this order: a, b, c. \n \n");
        scanf("%g %g %g", &aTwo, &b, &c);
        printf("\n --------------------------------- \n \n");


        //Parabola opening
        if(aTwo>0)  {
            printf("The parabola opens upward.\n ");
        }
        else    {
            printf("The parabola opens downward.\n");
        }


        //Axis of Symmetry
        float psy = b * -1;
        float dave = 2*aTwo;
        float axis = b/dave;
        axis*=-1.0;
        printf("The Axis of Symmetry is X = %g \n", axis);  //Axis of Symmetry


        //Y coordinate
        float one = pow(axis, 2);
        float two = one * aTwo;
        float three = b * axis;
        float four = c;
        float five = two + three + four;
        printf("The Y coordinate is %g \n", five);  //Y coordinate


        printf("The vertex is (%g, %g) \n", axis, five);    //vertex


        printf("The y-intercept is (0, %g) \n", c); //Y intercept

        //Max and Min
        if(aTwo>0)  {
            printf("The minimum is %g \n", five);
        }
        else    {
            printf("The maximum is %g \n", five);
        }

        //Range
        if(aTwo>0)  {
            printf("The range is Y ≥ %g \n", five);       //Minimum
        }
        else    {
            printf("The range is Y ≤ %g \n", five);   //Maximum
        }



        //Turn the standard form into vertex form using the vertex.
        //Vertex form is Y= a(x-h)² + K
        //standard form is Y= Ax² + Bx + C
        //aTwo=a, axis=h, five=k
        printf("The vertex form is Y = (%g)(x - (%g)) + (%g) \n", aTwo, axis, five);


    }

    return 0;
}