Parabolic Arch Properties and Equations

The video tutorial explains how to model an arch in the shape of a parabola, with a span of 196 meters and a maximum height of 14 meters. It covers deriving the equation of the parabola, identifying the vertex and intercepts, and solving for specific heights and distances from the center. The tutorial provides a step-by-step approach to finding the height of the arch 72 meters from the center and the distance from the center where the height is 2 meters.

What is the maximum height of the parabolic arch?

• 20 meters

• 18 meters

• 14 meters

• 10 meters

What is the span of the arch?

• 150 meters

• 196 meters

• 200 meters

• 100 meters

Where is the vertex of the parabola located?

• (0, 0)

• (0, 14)

• (-98, 0)

• (98, 0)

What are the x-intercepts of the parabola?

• (0, 14) and (0, -14)

• (0, 0) and (196, 0)

• (98, 0) and (-98, 0)

• (14, 0) and (-14, 0)

What is the form of the equation used to represent the parabola?

• y = ax^2 + bx + c

• x^2 = 4p(y - k)

• y = mx + b

• x = ay^2 + by + c

What is the value of 4P in the parabolic equation?

• 98

• 686

• -686

• -98

What is the height of the arch 72 meters from the center?

• 10.5 meters

• 6.44 meters

• 8.2 meters

• 12 meters

What is the equation used to find the height 72 meters from the center?

• x^2 = 4p(y - 14)

• x = 4p(y - 72)

• y = 4p(x - 72)

• y = 4p(x - 14)

At what distance from the center is the height of the arch 2 meters?

• 98 meters

• 72 meters

• 14 meters

• 9.73 meters

What is the significance of the plus or minus sign in the solution for x when the height is 2 meters?

• It denotes the span of the arch.

• It shows two possible distances from the center.

• It indicates two possible heights.

• It represents the maximum height.