Quadratic Functions Optimization

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

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

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

The graph of quadratic function f is shown on the grid.

f(x) = (x + 3)² − 5

Vertex: (a)  

y-intercept: (b)  

Axis of Symmetry: ​ (c)  

Minimum Value: (d)  

• (-3, -5)

• (0, 4)

• x = -3

• -5

• (-2, -4)

• (-6, 4)

• (4, 0)

• 4

• x = -5

• -4

Which answer choice describes  y = -3x² +7x - 2 accurately?

• opens up with a maximum

• opens up with a minimum

• opens down with a maximum

• opens down with a minimum 

If we have the equation here, can we graph and match?

(a)  

• F

• G

• H

• J

The graph of quadratic function f is shown on the grid.

Vertex: (a)  

y-intercept: (b)  

Axis of Symmetry: ​ (c)  

Minimum Value: (d)  

• (-3, -5)

• (0, 4)

• x = -3

• -5

• (-2, -4)

• (-6, 4)

• (4, 0)

• 4

• x = -5

• -4

The graph of quadratic function f is shown on the grid.

Vertex: (a)  

y-intercept: (b)  

Axis of Symmetry: ​ (c)  

Range : (d)  

• (-3, -5)

• (0, 4)

• x = -3

• x ≥ -5

• (-2, -4)

• (-6, 4)

• (4, 0)

• x ≥ 3

• x = -5

• -4

• 1

• 3

• 2

• 5

• 4