Most students learn to use the quadratic formula without ever understanding the neat way in which the quadratic formula can be viewed as a statement about symmetry. To do so requires looking at the quadratic formula not in the way it is usually seen as a single entity, but by splitting it up into two terms that can be interpreted graphically.
This is a quiz that puts a premium on using and understanding two techniques for finding zeroes and graphing: rewriting the function in intercept form and using the quadratic formula. In the first task students are required to show how they used factoring to construct a graph. In doing so they are confronted with the symmetry of the x-coordinate of the vertex with respect to the roots. In the second task students use the quadratic formula in order to find the same roots again. And they are asked to go further and interpret the meaning of the quadratic formula with respect to the graph.