Answer
$x$ -intercept at 1 unit.
Work Step by Step
We know that the standard form of the equation for a parabola with the vertex at $\left( h,\ k \right)$ is $f\left( x \right)=a{{\left( x-h \right)}^{2}}+k$.
Since the vertex of the given parabola is at $\left( 1,\ 2 \right)$ , we have $h=1$ and $k=2$. The value of $a$ must be greater than 0 as the graph opens upward.
The vertex is at $\left( 1,\ 2 \right)$, that is $h=1$ and $k=2$
Thus, the coordinate $\left( 1,\ 2 \right)$ lies in the first quadrant and the graph of the parabola opens upward.
