Find the equation for a parabola with vertex (2,-5)?

Question

But how would you write the equation? HELP!

Oh, and the parabola is supposted to have no x-intercept. (which means A is negative, right?)

Answer 1

The vertex is at (2,-5), and since the parabola has no x-intercept, the axis of symmetry must be x = 2, which is parallel to the y=axis. The equation for such a parabola is:
(x-2)^2b= 2p(y+5).

There are many parabolas which satisfy this equation depending on the value of p where p/2 is the distance from the vertex to the focus, and also the distance from the vertex to the latus rectum.

So pick an value of p you want, for example, p =6.
Then the equation becomes (x-2)^2 =12(y+5).

The focus is located at (2, -8) and the equation of the latus rectum is y = -2.

Answer 2

y=(x-a)^2 + b
y=-(x-2)^2 -5

This will cause it to have no x-intercept with vertex at (2,-5)