Parabola Word Problem

3/31/14

Graphing a Parabola with vertex (h,k)

y2 – 6y -2x + 8 = 0

X2 – 2x – 8y – 7 = 0

Graphing a Parabola with vertex (h,k)

Example 4

SPORTS A ball is thrown upward into the air with an initial velocity of 80 feet per second. The path of the ball can be modeled by the equation y = 80x – 16x2 which gives the height above the ground after x seconds. What is the maximum height the ball reaches?

The graph of the equation is a parabola which opens downward. Therefore, the vertex of the parabola would give us maximum height of the ball. To find the vertex, write the equation in standard form.

y = 80x – 16x2

y = -16(x2 – 5x)

y – 100 = -16 2 2554

x x

-1

16(y – 100) = 252

x

The standard form of the equation is 252

x = -1

16(y – 100).

The vertex of the equation is (52, 100).

Therefore, the ball reaches a maximum height of 100 feet. This occurs 2.5 seconds after the ball is thrown.

Finding the location of the receiver in a Satellite Dish.

Satellite dish is 24 feet in diameter at its opening and 4 feet deep in its center. Where should the receiver be placed?

Find the equation of a Parabolic Sound Dish.

If the parabolic sound dish the sideline crew is holding has a 2-foot diameter at the opening and the microphone is located 6 inches from the vertex, find the equation that governs the center cross section of the dish.

A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10 feet across at its opening and is 4 feet deep at its center, at what position should the receiver be placed?

The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 600 feet apart and 80 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point 150 feet from the center of the bridge?

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, how deep should the searchlight be?

A bridge is built in the shape of a parabolic arch. The bridge has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.

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