Graphing Quadratic Equations - Problem 6

One of the unique features of parabolas is that they are symmetric around the vertical line that passes through the vertex point. You can imagine a vertical "mirror line" that cuts the parabola into two halves. You can see this in a table of values, as well, provided you are clever in the way you set up your table. Here we explore how to find the vertex from vertex form and put that in the middle of the table with x values on either side of it. From there, we find the corresponding y values, using symmetry as a shortcut, and graph the parabola. This trick is preferable to plugging in randomly chosen x-values because we are including the "turning point," or vertex and finding points on either side of it to complete the symmetry.