Parabolas

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Write the equation of the *parabola* $y=x^{2}-4x-3$ 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**

$y=x^{2}-4x-3$

$y=\left(x^{2}-4x\right)-3$

$y=\left(x^{2}-4x+4\right)-4-3$

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

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

The *parabola* opens up words.

The *vertex* is given by $V\left(2,-7\right)$

The *focus* is given by $F\left(2,-\frac{27}{4}\right)$

The *directrix* is given by $y= -\frac{29}{4}$

The *axis of symmetry* is given by $x=2$