Quadratic Story Problems

A ball rolls down a slope and travels a distance represented by the given quadratic. What are the values of a, b, and c?

• a = 0.5, b = 6, c = 0

• a = 6, b = 0.5, c = 0

• a = 0, b = 0.5, c = 6

• a = 0, b = 6, c = 0.5

A ball rolls down a slope and travels a distance represented by the given quadratic, where d is the distance traveled and t is the time in seconds. When will the distance be 0?

• Only at the start (0 seconds)

• At the start and after 12 seconds

• t = 0 and t = -12

• Only after 12 seconds

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t² + 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

• 0.5 seconds

• 1 second

• 1.5 seconds

• 2 seconds

• 3 seconds

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

• 1 foot

• 5 feet

• 7 feet

• 8 feet

• 12 feet

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h = -4t² + 2t models her jump where h is her jump's height in feet t seconds after the mummy scares her. When did she reach her maximum height?

• 0.1 seconds

• 0.25 seconds

• 0.50 seconds

• 1 second

• 2 seconds

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation

h = -2t² + 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

• 2

• 4

• 9

• 10

• 15

Your cousin hit a golf ball with an initial velocity of 27 feet per second. The equation h = -6t² + 27t models the golf ball's height in feet t seconds after the ball was hit. How long after being hit did the ball reach maximum height?

• 1 second

• 2.25 seconds

• 3 seconds

• 4.5 seconds

• 5 seconds

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation

h = -4t² + 12t. How high did the soccer ball get?

• 1.5

• 3

• 5

• 9

• 15

A bottle rocket travels along a parabolic path modeled by the equation y = -21/25(x - 5)² + 21.  The distance traveled is measured in feet.  Determine the maximum height reached and the horizontal distance traveled by the rocket, assuming it leaves the ground at the point (0, 0)

• height 21 feet, horizontal distance 10 feet

• height 10 feet, horizontal distance 21 feet

• height 21 feet, horizontal distance 5 feet

• height 5 feet, horizontal didstance 21 feet

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

• 2 ft

• 80 ft

• 144 ft

• 64 ft