parabolas 6

Question

A building has an entry the shape of a parabolic arch 96 ft high and 18 ft wide at the base as shown below. 

 

Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Answer 1

The parabolic shape building height is 96 ft and width is 18 ft.

The parabola opens downward means a < 0 and the x part is squred.

The standard form of vertical parabola y = a(x - h)² + k

Vertex of parabola is (h ,k ) = (0,0)

y = a(x  - 0)² + 0

y = ax²

To find a value.

The height of parabola top to bottom is 96 ft means y coordinate is -96.

It's width from left to right is 18 ft means x coordinate is 18/2 = 9

Substitute (x, y) = (9 , -96) in y = ax².

-96 = a(9)²

-96 = 81a

a = -96/81

a = -32/27

Therefore the parabola equation is y = -32/27(x - 0)² + 0

y = (-32/27) x²