Parabolas

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Write the equation of the *parabola* $y=-2x^{2}-16x-8$ 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**

$y=-2x^{2}-16x-8$

$y=-2\left(x^{2}+8x\right)-8$

$y=-2\left(x^{2}+8x+16\right)+32-8$

$y=-2\left(x+4\right)^2+24$

$y-24= -2\left(x+4\right)^2$

The *parabola* opens down words.

The *vertex* is given by $V\left(-4,24\right)$

The *focus* is given by $F\left(-4,\frac{47}{2}\right)$

The *directrix* is given by $y= \frac{49}{2}$

The *axis of symmetry* is given by $x=-4$