Given z1 = 2 + sqrt 3i and z2 = 1 – sqrt 3i, what is the sum of z1 and z2?

Part A: The x intercepts are x coordinate that yield an output of zero:

We can use the quadratic formula to solve this equation:

So, the two solutions are

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So, the graph of the function passes trough the points (1, 0) and (3/2, 0)

Part B: A quadratic equation always represents a parabola. The parabola is facing up (it's "U" shaped) if a is positive, while it faces down ("n" shaped) if a is negative. In this case a is positive, so the vertex is a minimum.

We can find the x coordinate of the vertex using the formula

And plug that value to find the y coordinate:

Part C: We already did pretty much everything we could have done to plot the graph. We know the vertex and the x-intercepts, so you know that the parabola will have to pass through those points. Remember that the vertical axis of symmetry passes through the vertex, and if you want you can sample some more point to be more accurate.