Parabolic problem

Question

An arch over an entrance is semicircular with an opening that is 5 feet wide. Write an equation that models that arch.

Answer 1

If the opening is 5 feet wide, I assume you mean from the center point of the straight edge to the top of the arch. Thus the radius of the arch is 5 feet. Since it is on top, I assume the arch points upward and so the equation is y = √(25-x²)

This equation can be found from the equation of a circle (x-h)²+(y-k)²=r². The point (h,k) is the center of the circle (here we defined the center to be (0,0)) and r=5 so r²=25. Thus x²+y²=25. Then you solve for y but only use the positive answer since we're talking about the top semicircle.