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For each equation in parts (a) through (d) below, determine the input value that gives the smallest possible output. In other words, what is the ‑value of the lowest point on the graph? What is the input value that gives the largest possible output (or the ‑value of the highest point on the graph)?

  1. Are there any -values that yield a negative number?

    It is impossible for the output to be negative in this case. What is the lowest value can be? Can ?

  1. Does this parabola open upward or downward?

    It opens upward. Therefore, there will be a smallest output. What input yields the smallest output?

  1. See part (a).

  1. See part (b). Notice the negative sign in front of the term. How does that change the parabola?

  1. For each function above, where on its graph is the maximum or minimum point?