Graphing Quadratic Function

          Actually there is the simplest way in graphing quadratic function y=ax²+bx+c. Just input the value of x to the function to get the value of y then you will get the point. Repeat it to get some point. Plot those points on the Cartesian diagram. Draw a smooth curving line passing the plotted point.

        However this way often brings you to the misconception about the graph because we do not know specifically how the graph will be. There are some steps below that you have to know to graph the quadratic function correctly.

1.  

     Take a look for the value of a in ax²+bx+c. If a were positive so the graph will right-side-up. And if a were negative so the graph will be upside-down.

2.     

    Determine the determinant value of its quadratic function, D=b²-4ac

·         For D < 0, the graph will not across the x-axis

·         For D = 0, the graph will drag in the x-axis in one point

·         For D > 0, the graph will across the x-axis in two points

3.     

    Find the vertex of the graph (x,y).

·         x = -b/2a

·         y = -D/4a

4.   

          Find the interception point

·         y-intercept, the value of y when x=0

·         x-intercept, the value of x when y=0

5.  

         Find additional points; input the value of x in order to get the value of y.

6.  
          Label the vertex, interception point and plot the additional point, then smoothly do the 

    graph through vertex label and plotted point.