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 using the x value -b/2a and plugging that back in to find y. We sketch the vertex along with the vertical axis of symmetry. We find the x-intercepts (if there are any) by factoring, but if factoring didn't work, we would use the quadratic formula. 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 five points to get a sketch of the parabola.
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