Alexandra A.

asked • 08/13/20# How many parabolas can you fit? Write the functions for each one

**A room with dimensions 20 feet by 26 feet is to be used to host a meeting. Under the CDC guidelines, we need to design the seats to be six feet apart. Janet suggested to put the attendees on a parabola-like setting, with the zeros of the function on one edge of the room. The vertices of the parabolas should also be 6 feet apart.**

**How many parabolas can you fit? Write the functions for each one.**

## 1 Expert Answer

This is a fun question.

To get a parabola that is as wide and long as the room:

f(x) = -0.26x^{2} + 26

This will put your y intercept at the "c" your equation, 26. In order to fit the 20ft wide room, our x intercepts are at -10 and 10. Since we know we want these intercepts (y=26, x=-10, x=10) we want our "a" term, the cofactor for x^{2}, to cancel out our "c" value. -0.26*10*10 = -26.

From here, just subtract 6 from your "c" until you don't have any space between your curve and the x-axis.

g(x) = -0.26x^{2} + 20

h(x) = -0.26x^{2} + 14

i(x) = -0.26x^{2}+ 8

j(x) = -0.26x^{2} + 2

There you go. Parabolic social distancing.

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Mark M.

Why non a parabola instead of a grid? Are more then one parabola used at a time? How do the seats get 6-feet apart on the parabola?08/14/20