A parabolic archway is 12 meters high at the vertex. At a height of 10 meters, the width of the archway is 8 meters. How wide is the archway at ground level? (Round your answer to one decimal place.)

Answer 1

Draw and label a diagram

Vertex: (0, 12)

Point: (4, 10)

y = a(x - h)² + k

10 = a(4 - 0)² + 12

-2 = a(16)

-1/8 = a

y = (-1/8)(x - 0)² + 12

0 = (-1/8)x² + 12

-12 = (-1/8)x²

96 = x²

±√96 = x

The width is 2√96