Parabolas

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Write the equation of the *parabola* $y=x^{2}+18x+6$ 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**

$y=x^{2}+18x+6$

$y=\left(x^{2}+18x\right)+6$

$y=\left(x^{2}+18x+81\right)-81+6$

$y=\left(x+9\right)^2-75$

$y+75= \left(x+9\right)^2$

The *parabola* opens up words.

The *vertex* is given by $V\left(-9,-75\right)$

The *focus* is given by $F\left(-9,-\frac{299}{4}\right)$

The *directrix* is given by $y= -\frac{301}{4}$

The *axis of symmetry* is given by $x=-9$