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For each equation, what input value will produce 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)?  


    Are there any -values that yield a negative number?

    It is impossible for to be negative in this case. In turn, what is the lowest value can be? Can equal ?

    When is equal to , is equal to , which is the smallest possible output.


    Does this parabola open upward or downward?

    It opens upward. Therefore, there will be a smallest output.

    Lowest point: ,


    See part (a).


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