Parabolas
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Question

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 $x=-9$