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

See below in bold.

Explanation:

We can write the equation as

y = a(x - 28)(x + 28) as -28 and 28 ( +/- 1/2 * 56) are the zeros of the equation

y has coordinates (0, 32) at the top of the parabola so

32 = a(0 - 28)(0 + 28)

32 = a * (-28*28)

32 = -784 a

a = 32 / -784

a = -0.04082

So the equation is y = -0.04082(x - 28)(x + 28)

y = -0.04082x^2 + 32

The second part is found by first finding the value of x corresponding to y = 22

22 = -0.04082x^2 + 32

-0.04082x^2 = -10

x^2 = 245

x = 15.7 inches.

This is the distance from the centre of the door:

The distance from the edge = 28 - 15.7

= 12,3 inches.