Parabolas

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Write the equation of the *parabola* $y=-2x^{2}-4x-9$ 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**

$y=-2x^{2}-4x-9$

$y=-2\left(x^{2}+2x\right)-9$

$y=-2\left(x^{2}+2x+1\right)+2-9$

$y=-2\left(x+1\right)^2-7$

$y+7= -2\left(x+1\right)^2$

The *parabola* opens down words.

The *vertex* is given by $V\left(-1,-7\right)$

The *focus* is given by $F\left(-1,-\frac{15}{2}\right)$

The *directrix* is given by $y= -\frac{13}{2}$

The *axis of symmetry* is given by $x=-1$