Name ______ACC Math

Date ______Parabola Word Problems Period ______

Parabola Word Problems Math8 Notes

1) Devon and Adrie are practicing for their softball game. The path formed by Devon’s ball is marked by the solid lines; the path formed by Adrie’s ball is marked by the dotted lines. Let x represent time and y represent the height in meters. A) How high does Devon throw the softball?

B) How much higher does Arie throw the softball than Devon?

C) How long did it take Devon’s softball to hit the ground?

D) If Adrie’s and Devon’s softballs had equal flight times, what does this tell you about the force at which Adrie threw the softball compared to Devon’s force?

2) To celebrate July 4, the town of Trigon has hired Pyro-Tech, Inc. to launch fireworks at a baseball field in the center of town. The rockets can be fired with an initial upward velocity of 64 feet per second.

Pyro-Tech uses a function that estimates the rocket’s height above the ground (y) in terms of the time (x) since the launch. If x is in seconds and y is in kilometers, then y = - ½ x2 + 8.

X / Y

A) How long will it take the fireworks to reach their highest point?

B) How high are the fireworks?

C) How long after the launch will the debris hit the ground?

Parabola Word Problems

1) Ryan and Emilio are practicing for their lacross tournament. The path formed by Ryan’s ball is marked by the solid lines; the path formed by Emilio’s ball is marked by the dotted lines. Let x represent time and y represent the height in meters.

A) How high does Emilio launch the ball?

B) How much longer did Emilio’s ball stay in the air (than Ryan’s ball did)?

C) How long did it take Ryan’s ball to hit the ground?

D) How much higher does Emilio launch the ball than Ryan?

E) Based on this information, can we make any conclusions about the force at which Emilio and Ryan threw launched balls?

2) Each of the “golden arches” at McDonald’s restaurant is in the shape of a parabola. Each arch is modeled by y = -x2 + 6x, where h is the height of each arch (in feet) at a distance x (in feet) from one side.

X / y
0
1
2
3
4

A) How wide is each arch?

B) How high is each arch?

C) How wide is the base of the entire “M”?


3) A tennis ball is thrown into the air and follows a path modeled by

y = -x2 + 2x + 3, where y represents the height in meters of the ball and x represents time.

x / Y

A) How long will it take the tennis ball to reach its highest point?

B) How high does the tennis ball go?

C) How long after the tennis ball is thrown will it hit the ground?

4) Dave and Ms. Kuehn are in a diving competition. The path formed by Dave is represented by the solid lines; the path formed by Ms. Kuehn is represented by the dotted lines.

A) How deep does Ms. Kuehn dive?

B) How long does it take Ms. Kuehn to resurface?

C) How much deeper does Dave dive than Ms. Kuehn?

D) How much longer does Dave stay under water?

E) What can we say about Ms. Kuehn’s diving abilities?

(don’t answer that question J)