How Do We use the discriminant to Find the Number of Solutions To a Quadratic Equation?

The solutions to a quadratic Equation is when the Parabola touches the X- axis which are also called the "roots".

 The Discriminant is B^2 - 4AC

 If B^2 - 4ac > 0 you`ll get two solutions
 If B^2 - 4ac = 0 you`ll get one solution
 If B^2 - 4ac < 0 you`ll get no solution

For example :
                         X^2 + 6X + 9 = 0
A = 1                  B^2 - 4ac = ?
B = 6                   6^2 - 4(1)(9)
C = 9                    36 - 36 = 0

         (One solution) because its equal to Zero

Another example:
                              -16x^2 + 11x - 11 = 0
A = -16                     B^2 - 4ac =?
B = 11                      11^2 - 4(-16)(-11)
C = -11                    121-+ 64(-11)
                                   121 + -704
                                          -583
           (NO solution) because its less then Zero

   Example:
                      5x^2 + 2x - 10 = 0
A=5                b^2 - 4ac
B=2                   2^2 - 4(5)(-10)
C=-10                 4- 200
                             204
           ( Two solutions) because its greater then Zero

How Do We Work with quadratics?

The first thing that you should think of when you think of quadratics is the 
      Quadratic Equation:
                 
So if you have the equation x^2 + 2x - 1

• First you have to find the value of A, B and C
• The value of A is in front of the first x 

            A = 1

• The value of B is in front of the second X                 

           B = 2
  The value of C is the number without an x after it
            C = -1
           Step 1: plug in      
        Step 2 : simplify