An arch in the shape of a parabola is 10 feet wide at its base and 25 feet tall. How wide is the arch 9 feet up?

Answer 1

Draw and label a diagram.

Vertex at (0, 25)

x-intercepts at (-5, 0) and (5, 0)

f(x) = ax² + 25

f(5) = a(5)² + 25

0 = 25a + 25

-25 = 25a

-1 = a

f(x) = -x² + 25

9 = -x² + 25

-16 = -x²

16 = x²

f(x) = -20x² + 25

±4 = x

The arch is 8 feet wide.

Answer 2

An arch in the shape of a parabola is 10 feet wide at its base and 25 feet tall. How wide is the arch 9 feet up? the answer is 8 ft