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Write the equation of the parabola $y=-2x^{2}+1$ in the standard form. Then determine the vertex, focus, directrix and the axis of symmetry of the parabola. Also, state which way the parabola opens.



$y-1= -2\left(x-0\right)^2$

The parabola opens down words.

The vertex is given by $V\left(0,1\right)$

The focus is given by $F\left(0,\frac{1}{2}\right)$

The directrix is given by $y= \frac{3}{2}$

The axis of symmetry is given by $x=0$