Question

Using the given information, give the vertex form equation of each parabola.

Answer 1

Answer:

Step-by-step explanation:

If you plot these points on a coordinate plane, you will see that they both lie on the same horiztonal line, y = -10, with the focus 1/4 to the right of the vertex.  This information tells you a ton of stuff.  First, it tells you that, since a parabola "hugs" the focus, this parabola opens to the right and is of the form x = y-squared.  This equation is

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

The information also tells us that p (the distance between the vertex and the focus) is .25.  h is the "x" coordinate of the vertex and k is the "y" coordinate of the vertex, so h = -1, and k = -10.  Filling in our formula:

$4(.25)(x+1)=(y+10)^2$

Simplify the left to

$1(x+1)=(y+10)^2$ and solve for x:

$x=(y+10)^2-1$