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 upward with vertex at and is the minimum value of f.
The standard form of the quadratic function is . The graph of this function turns out to be a parabola with vertex set . The parabola opens upward if and opens 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 and notice that , and .
From the definition used above, which is greater than zero and therefore the parabola opens upward.
Notice that the vertex is at which is .
Since , the minimum value of f is at is,
Therefore, at the function has a minimum value.
Hence, the graph of is a parabola that opens upward with vertex at and is the minimum value of f.
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