The dishwasher marlin wants costs $720. this week only, the dishwasher is discounted by 25%. marlin must pay 6% sales tax. which saves the most money?

A parabola is a figure with one vertex, and extending in curved lines at both sides creating an opening. It is stated here that the vertex is placed at the origin, thus it is at (0,0). It is also said that the antenna is placed ABOVE the vertex, so the parabola is opening upwards. The general formula for this is:

(x-h)^2 = 4a(y-k), where the origin is (h,k) therefore h=0 and k=0; a is the distance of focus to the vertex. Let's use the value of the depth and the diameter to fully define the equation. Since the depth is 2 feet, the diameter is 4, and the origin is at (0,0), then the parabola must pass the coordinates (4,2) and (-4,2) situated at opposite sides of each other. Let's use one of these (any of these two will yield the same answer):

(4-0)^2 = 4a(2-0)
4a = 8
a = 2

The lactus rectum of the parabola in the equation is 4a. Therefore, the length of the lactus rectum is 8 units. Then, the antenna should be placed at the focus which is 2 units above the vertex. The standard form of the parabola would then be: x^2 = 8y. The defining feature of a parabola is when its equation only has either x^2 or y^2, but not both.