Answer
The vertex is $(\displaystyle \frac{7}{2},-\frac{29}{4})$
The axis of symmetry is $x=\displaystyle \frac{7}{2}.$
The minimum function value is $-\displaystyle \frac{29}{4}$.
Work Step by Step
$f(x)=(x-\displaystyle \frac{7}{2})^{2}-\frac{29}{4}$
$a=1$
$h=\displaystyle \frac{7}{2}$
$k=-\displaystyle \frac{29}{4}$
The vertex is $(h, k)$, and the axis of symmetry is $x=h.$
For $a\gt 0$, the minimum function value is $k$.
For $a\lt 0$, the maximum function value is $k.$
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The vertex is $(\displaystyle \frac{7}{2},-\frac{29}{4})$
The axis of symmetry is $x=\displaystyle \frac{7}{2}.$
Since $a\gt 0$, the minimum function value is $-\displaystyle \frac{29}{4}$.