To fill: The statement “The graph of is a parabola that opens _____________ with vertex at and is the (minimum/maximum) _____________ value of f ”.
The graph of is a parabola that opens downward with vertex at and is the maximum value of f.
Standard form of a quadratic function:
The standard form of a quadratic function is , where is the vertex of the parabola. And the parabola opens upward if or downward if .
The maximum or minimum value of f occurs at . If , then the maximum value of f is and if , then the minimum value of f is .
Compare the standard form of quadratic equation with .
Then, , and .
From the definition used above, which is less than zero and therefore the parabola of the function opens downward.
Thus, the vertex is at which is .
Since , the maximum value of f is at is,
Therefore, at the function has a maximum value.
Hence, the graph of is a parabola that opens downward with vertex at and is the maximum value of f.
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