?Find the vertex, focus, and directrix of the parabola and sketch its graph. (x ? 3) 2 =

Step 1 of 3

Consider the given data as follows.

The equation of the parabola is \((x-3)^{2}=8 (y+1)\).

The vertex, focus, and directrix of the parabola \({{x}^{2}}=4py\) is defined as \(\left( 0,0 \right)\), \(\left( 0,p \right)\), and \(y=-p\), respectively.

Shifting the graph of the parabola \({{x}^{2}}=4py\), h units in the direction of the positive x-axis and k units in the direction of the positive y-axis are given the graph of the parabola \({{\left( x-h \right)}^{2}}=4p\left( y-k \right)\).

So, it can be concluded that the vertex, focus, and directrix of the parabola \({{\left( x-h \right)}^{2}}=4p\left( y-k \right)\) will be \(\left( h,k \right),\ \left( h,\ p+k \right)\), and \(y=-p+k\), respectively.