Quadratic Functions: Optimization

Farmer Jo has 32 square meters of land in which to make an enclosure for bunnies, chicks, and penguins. (see picture)

Choose the equation that represents this information.

• $2x+4y=32$

• $2x+2y=32$

• $xy=32$

• $A=3xy$

Farmer Jo has 32 square meters of land in which to make an enclosure for bunnies, chicks, and penguins.  There will be fencing put in around the entire enclosure and in the middle (as pictured) to create 3 sections, what dimensions should the overall enclosure be in order to use the least amount of fence?

• The overall enclosure should be 8m by 8m

• The overall enclosure should be 8m by 4m

• The overall enclosure should be 32m by 1m

• It's impossible to tell

A farmer wants to construct a rectangular pigpen using 400m of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

• 100m x 200m

• 102m x 196m

• 50m x 300m

• 50m x 175m

We need to enclose a field with a fence. We have 500 meters of fencing material and a building is on one side of the field so we won't need any fencing on that side. Determine the dimensions of the field that will enclose the largest area.

• x=250m, y=125m

• x=150m, y=200m

• x=125m, y=100m

• x=200m, y=150m

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

• After 5 seconds

• After 1 second

• After 2 seconds

• After 3 seconds

The height of a water balloon that is launched into the air is given by h(t) = -5t² + 40t + 2. From what height was the balloon released?

• 2 meters

• 5 meters

• 40 meters

• 20 meters

Tags

CCSS.HSA.CED.A.1

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

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t² + 45

When is the ball at ground level?

• only at t = 0 seconds

• only at t = 3 seconds

• only at t = 9 seconds

• at both t = 0 seconds and t = 3 seconds

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t² + 90t gives the height h of the ball after t seconds.
How many seconds will it take the ball to hit the ground?

• 126.56 ft
• 5.625 sec
• 2.81 sec
• 0 ft

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

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