Question

The outer door of an airplane hangar is in the shape of a parabola. The door is 120 feet wide and 90 feet high. (i)Find the equation describing the door’s shape. (3) (ii)If you are 6 feet tall, how far must you stand from the edge of the door to keep from hitting your head? (2)

Answer 1

Explanation:

So this will be an upside down parabola....the leading coefficient (for x^2 ) will be negative ...

Vertex at 60,90 <=====given

Vertex form y = a (x-h) ^2 + k

y = a ( x -60)^2 + 90 to find 'a' substitute in a point on the parabola...I'll use 0,0

0 = a ( 0-60)^2 + 90 shows a = - 1/40

so the equation is y = -1/40 ( x -60)^2 + 90

( or expanded to y= -1/40 x^2 + 3x )

Solve for 'x' when y = 6 ft ( to keep from hitting your head)

6 = -1/40x^2 +3x

0 = -1/40 x^2 + 3x - 6 Use Quadratic Formula to find x = ~ 2 feet