Can someone please help me :((

Since the parabola is 'inverted', it has the form;

4p(x - h) = (y-k)^2

Where p is the directrix.

Your equation becomes:

x=-\frac18 y^2

-8x=y^2

-8(x - 0)x=(y-0)^2

You get:

4p = -8

So, p = -2.
Since your parabola opens to the left, the directrix should be on the right, and since the vertex is at (0, 0), the directrix should also be positive

The directrix is given by h-p, that is; 0 + 2 = 2.

The equation of the directrix is therefore x = 2.

Thank you so much !

You're welcome :)

Would you be able to help me with basic trigonometry ?

A surveyor measures the angle of elevation to a point on a mountain that is 6 miles away to be 15 degrees. The vertical change in elevation from the point where the surveyor is standing to the point on the mountain is how many miles?

I need to round to the nearest hundredth of a mile?

Please help :)

Have a drawing in front of you to help you.

You have a right angled triangle, with a base of 6 miles, and an angle of 15 degrees.

From the tangent ratio, we know that:

tan(15^o) = \frac{OPP}{ADJ} = \frac{h}{6}

where I call 'h' the height of the mountain. Find 'h' :)