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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