Find properties of a parabola from equations Geometry

Determine the vertex of the following parabola:

y=2\left(x-1\right)^2+1

\left(1{,}1\right)

\left(1,-1\right)

\left(-1{,}1\right)

\left(-1,-1\right)

Determine the focus of the following parabola:

y=\left(x-2\right)^2+3

\left(2,\dfrac{13}{4}\right)

\left(\dfrac{13}{4},2\right)

\left(-2,\dfrac{13}{4}\right)

\left(2,\dfrac{13}{2}\right)

Determine the focus of the following parabola:

x=\dfrac{1}{2}\left(y+1\right)^2+2

\left(\dfrac{5}{2},-1\right)

\left(-1,\dfrac{5}{2}\right)

\left(\dfrac{17}{8},-1\right)

\left(-1,\dfrac{17}{8}\right)

Determine the vertex of the following parabola:

x=y^2+6y+10

\left(1,-3\right)

\left(-3{,}1\right)

\left(1{,}3\right)

\left(3{,}1\right)

Determine the vertex of the following parabola:

y=2x^2+16x+40

\left(-4{,}8\right)

\left(4{,}8\right)

\left(-4,-8\right)

\left(-8{,}4\right)

Determine the focus of the following parabola:

y=x^2+4x+5

\left(-2,\dfrac{5}{4}\right)

\left(2,\dfrac{5}{4}\right)

\left(\dfrac{5}{4},-2\right)

\left(\dfrac{5}{4},2\right)

Determine the focus of the following parabola:

x=y^2+6y+12

\left(\dfrac{13}{4},-3\right)

\left(-\dfrac{13}{4},-3\right)

\left(-\dfrac{13}{4},3\right)

\left(\dfrac{13}{4},3\right)