How do we Graph Parabolas?

Graphing the Parabola y = ax2 + bx + c


1.    Determine whether the parabola opens upward or downward.


                 a.    If a is positive, it opens upward.
                b.    If a negative, it opens downward.


2.    Determine the vertex.
             a.    The x-coordinate is .
                 b.    The y-coordinate is found by substituting the x-coordinate, from Step 2a, in the equation                                                     y = ax^2 + bx + c.


3.    Determine the y-intercept by setting x = 0.

by determining all the key features of the graph. That is, find the vertex, the x- and y-intercepts (if any), and additional points if needed. Find the domain and range of the function.

Opens upward since the coefficient of the x² is positive  

4.    Determine the x-intercepts (if any) by setting y = 0, i.e., solving the equation 
       ax2 + bx + c = 0.


5.    Determine two or three other points if there are no x-intercepts.



For Example:

Graph  

Vertex:  and  So the vertex is (3, -4).

y-intercept:  The y-intercept is (0,5).

x-intercepts:

                            

The x-intercepts are (5,0) and (1,0).

        Points plotted on grid below:

 Then connect the points with a smooth curve.
Here is A video to help you understand better how to graph a Parabola.