Final answer:
The question involves finding the equation of a parabola given the vertex and focus coordinates. The parabola opens to the right, with a vertex at (-(11)/(4), -2) and a focus at (-3, -2), indicating a horizontal parabola. The equation can be determined using the distance from the vertex to the focus.
Step-by-step explanation:
The question indicates it is dealing with a parabola in a coordinate plane, given that it specifies a vertex and a focus, which are elements in the definition of a parabola. Since the coordinates of the vertex and the focus are provided, one can determine the directrix and the equation for this parabola. The standard form for the equation of a parabola is either (y - k) = 1/(4p)(x - h)^2 for a parabola opening left or right, or (x - h) = 1/(4p)(y - k)^2 for a parabola opening up or down, where (h,k) is the vertex and p is the distance from the vertex to the focus. Additionally, p is also the distance from the vertex to the directrix.
Given the vertex at (-(11)/(4),-2) and the focus at (-3,-2), we can see that the parabola opens to the right since the y-coordinates are the same and the focus has a greater x-coordinate than the vertex. The distance p is therefore 5.4 cm from the axis (using the SEO keyword context), which equates to 5.4/100 meters in SI units, as the distances provided in the question appear to be in centimeters.
To find the equation, we set up the form (y - k)^2 = 4p(x - h). Using the vertex (h, k) = (-(11/4), -2), and p = (5.4/100) meters, the equation in terms of meters should be adjusted accordingly if needed. To convert the vertex from a mixed number to an improper fraction, we calculate h as -11/4 or -2.75 in decimals, and thus we can write the equation for the parabola in its respective units.