Hello, 14041471!
Write an equation for the parabola whose vertex is (4, 3),
axis of symmetry is and the measure of the latus rectum is 4;
I also need to draw this parabola.
You might start with a sketch . . . Code:

 *
 *
 * :
 (4,3) * p :
 +    o   o  
 V * :F
+*:
 *
 *

We're expected to know the following . . .
Since the axis of symmtetry is horizontal, the parabola opens "sideways."
Since , the parabola opens to the right.
The general form is: .
. . where is the vertex,
. . and is the focal distance (distance from vertex to focus).
Fact: the length of the latus rectum is
. . . . We have: .
Since the vertex is: .
. . the equation is: .