Graphing Quadratic Equations - Problem 11

There are five key points that can often be enough to sketch a parabolic function: the y intercept, x intercept(s), vertex, and reflection of the y-intercept across the axis of symmetry. Here we find the vertex of a parabola from vertex form and sketch it along with the vertical axis of symmetry. In this case, the vertex happens to be the only x-intercept. The y-intercept can always be found by letting x = 0 in the function. A fifth point rounds out the symmetry when the y-intercept is reflected across the axis of symmetry line. We connect these points to get a sketch of the parabola. Here is a situation where our "5 point" method of graphing is only a "3 point" method.