A parabola opens toward to the location of focus with respect to the vertex.
When the vertex and focus has same y-values, it implies that the parabola opens sideways (left or right).
When the vertex and focus has same x-values, it implies that the parabola may opens upward or downward.
The given focus of the parabola `(0, 7/4)` is located above the vertex `(0,0)` . Both points has the same value of `x=0` .
Thus, the parabola opens upward. In this case, we follow the standard formula: `(x-h)^2=4p(y-k)` . We consider the following properties:
vertex as `(h,k)`
focus as `(h, k+p)`
directrix as `y=k-p`
Note: `p` is the distance of between focus and vertex or distance between directrix and vertex.
From the given vertex point `(0,0)` , we determine h =0 and k=0.
From the given focus `(0,7/4)` , we determine `h =0` and `k+p=7/4` .
Plug-in ` k=0` on `k+p=7/4` . we get:
Plug-in the values: `h=0` ,`k=0` , and `p=7/4` on the standard formula, we get:
`x^2=7y` as the standard form of the equation of the parabola with vertex `(0,0)` and focus `(0,7/4)` .