Answer to Question #124635 in Geometry for frank

Question

1. A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head?

Answer 1

for equation of parabolic shape for the door

(x-h)² = -4a (y-k)

Now x=28 from the sketch and y =0 ,h=0 ,k=32

(x-h)² = -4a(y-k)

(x-0)² = -4a (y-32)

(28-0)² = -4a (0-32)

(28)² = -4a (-32)

28x28 = 4a x 32

a = 28x28/(4x32)

a=49/8

now for distance

If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head?

a=49/8 k= 32 and, y=22

x² = -4a (y-k)

x² = - 4 (49/8) (y-32)

x² =-49/2 (22-32)

x² = -49/2(-10)

x² = 490/2

x² = 245

x= √245

x=15.65 inch