Parabolas

You can view as many worked out examples as you want. First you are shown the question. Click Show Answer to view the answer.
Click Show another Example to view another example. The best way to master mathematics is by practice. But practice requires time.
If you don't have the time to practice, you can always view many practice problems completely worked out and become good at it too.

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

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

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

$y=-2\left(x^{2}+x+\frac{1}{4}\right)+\frac{1}{2}-8$

$y=-2\left(x+\frac{1}{2}\right)^2-\frac{15}{2}$

$y+\frac{15}{2}= -2\left(x+\frac{1}{2}\right)^2$

The *parabola* opens down words.

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

The *focus* is given by $F\left(-\frac{1}{2},-8\right)$

The *directrix* is given by $y= -7$

The *axis of symmetry* is given by $x=-\frac{1}{2}$