Answer:
In vertex form the equation is
In standard form the equation is
Step-by-step explanation:
The equation of the directrix tells us that this is an x-squared parabola. Because the directrix is above the vertex, the parabola will open downward. The vertex form of this equation is:
where p is the number of units between the directrix and the vertex. The number of units here is .5 or 1/2. Filling in the coordinates of the vertex and the p value of 1/2:
Simplifying we have:
Divide both sides by 2 to get:
Add 2 to both sides to get the final vertex form:
If you want that in standard form, you first need to expand the squared term to get:
Order of operations tells us that we have to distribute in the -1/2 first to get:
which simplifies to the standard form: