Graphing Quadratic Equations - Problem 9

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 letting x = -b/2a. Since "b" is zero, the x-value of the vertex will also be zero, and our axis of symmetry will be the y-axis. We find the x-intercepts here by isolating the x^2 and square rooting both sides. Alternatively, we could factor or use the quadratic formula. The y-intercept can always be found by letting x = 0 in the function, but in this case, it ends up being the same point as the vertex. Hence, we can't reflect it across the axis of symmetry, either. This is an example where our "5-point" method becomes a "3-point" method for sketching a parabola.