write the equation of the parabola given v(3,1),F(3,-3)....?

Question

v stands for vertex and f stands for focus...

Answer 1

Find the equation of the parabola given the vertex (3,1) and the focus (3,-3).

Since only the y values change between the vertex and focus, the parabola opens vertically. The equation of a vertical parabola with vertex (h,k) in vertex form is:

4p(y - k) = (x - h)²

The directed distance from the vertex to the focus is p.

p = -3 - 1 = -4

Since p is negative the parabola opens downward. Now we have all the values and can write the equation of the parabola.

4p(y - k) = (x - h)²

4*(-4)(y - 1) = (x - 3)²

-16(y - 1) = (x - 3)²

Answer 2

(y - 1) = - (1/16)(x - 3)^2

Answer 3

I'm telling your teacher.