" How Do We Calculate Quadratic Inequalities? "

                      Calculating quadratic inequalities are quite easier than it sounds !
                 You can solve quadratic equations in 3 short, easy, and simple steps !
 The first step in solving quadratic inequalities is taking a inequality like "  y > 2x^2 " and turning it into a equation by replacing the inequality sign with an equal sign. 
                    so " y > 2x^2 " turns into " y = 2x^2 " 

     The second step is to graph the equation " y = 2x^2 " using a dashed line for  < or > and a solid line for < or >.        

     The third step would be to choose a test point, in or outside the parabola.
               Let's use the test point ( 2, 0 ) . You plug the test point into the inequality. 
                                   y > 2x^2     
                            0 > 2(2)^2
                            0 > 2(4)
                            0 > 8   <-- This is false : 0 is not greater than 8. 
    The last step would be to shade in the side (whether the inside of the parabola or outside the parabola).

 * not accurate to problem , just visual example * 

 * where ever your test point is, if it is true you shade the whole thing . If it is false than you should the opposite * .      
            The final answer to the inequality is the shaded area 

NOW TRY IT YOURSELF : 
                      USING THE INEQUALITY : " y > x^2 - 1 " 
                                                                                                                                     

" How Do We Complete the Square ? "

Completing the square is as easy as it sounds !
                 Let's consider the equation: "  x^2+6x+2=0 "
    The first step in completing the square is is moving the constant term, which in this case is 2, to the other side of the equation. The equation now looks like: "  x^2+6x+__= -2 "
     The second step is to take the coefficient of the middle term, which is 6 in this case, and dividing it in half and squaring it. So 6 divided in half is 3. 3 squared is 9.
     The third step is to add 9 to both sides of the equation. " x^2+6x+9 = -2+9 "
                                                                 simplified to :      x^2 + 6x + 9 = 7
  The fourth step is to factor the trinomial : (x+3)^2 = 7
 The next step is to find the square root of both sides : The square root of (x+3)^2 is (x+3) .

      The square root of 7 can be either negative or positive , so its written like: +-√7
                                                                                


                                         
    The last step is to subtract 3 from each side : (x+3) =  +- √7
                                         - 3         - 3





      The final answer you get is : x= -3 +- √7




Now You Try It :
                                  x^2 + 8x + ___ = 7