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For each equation in parts (a) through (d) below, find the input value that gives the smallest possible output. In other words, find the -value of the lowest point on the graph. Then find 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 to be negative in this case. What is the lowest value  can be? Can equal ?

  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. Where on the graphs of each of the above equations would you find the points with the smallest or largest -values?