Quadratic Systems and Word Problems

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

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

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

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.10

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

• 2.625

• 6.25

• 100

• 200

• 210.25

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t  
When will the object reach its maximum height?

• 4 ft
• 0 seconds
• 0 ft
• 4 seconds

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

Find the solution.

• (4,2) and (0,9)
• (-4,-1) and (2,5)
• (5,3) and (5,2)
• (-4,2) and (5,9)

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.11

Find the solution.

• (6,4) and (3,1)
• (-2,7) and (5,2)
• (5,4) and(-2,-5)
• (1,-1) and (4,2)

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Find the solution.

• (56,7) and (25,1)
• (35,2) and (-12, 15)
• (15,89) and (2,-2)
• (30,4) and (-45, 5)

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.11

Find the solution.

• (3,18) and (-4, 15)
• (5,2) and (5,-9)
• (0,0) and (0,0)
• (-4,2) and (-4,2)

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.11

What are the solutions to this quadratic/ linear system?

• (-2, 0) and (3,0)

• No Solutions

• -6 and -10

• (1,-6)

Tags

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7