Parabolas

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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.

**Answer**

$y=-2x^{2}+1$

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

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 $x=0$