Modeling Quadratic Functions

Ms. Hodge's lawn company's charges for landscaping includes the cost of the soil and flat rate fee for labor. The length of the flower bed is 3 feet longer than its width and the charges for the job are 9.5x(x + 3) + 500. Select the true statement.

• x(x + 3) represents the flat rate the company charges for labor

• x(x + 3) represents the width of the flower bed

• x(x + 3) represents the amount of materials needed

• x(x + 3) represents the area of the flower bed

Select the statement that is true for the function f(x) = 2x² + 8x - 24.

• The minimum value is -32.

• The minimum value is 32.

• The maximum value is 32.

• The maximum value is -32.

The maximum value of function f is ______ the maximum value of function g.

• greater than

• less than

• equal to

The y-intercept of function f is _____ the y-intercept of function g.

• greater than

• less than

• equal to

Considering the parent function f(x) = x², describe the transformations applied to graph the function g(x) = (x - 2)² + 3.

• 3 units up

• 3 units down

• 3 units right

• 3 units left

For which interval is the graph always decreasing?

• 0 < x < 1

• 0 ≤ x ≤ 1

• 1 ≤ x ≤ 3

• 1 < x < 3

Considering the parent function f(x) = x², describe the transformations applied to graph the function g(x) = (x - 4)² + 7.

• 4 units right, 7 units down

• 4 units right, 7 units up

• 4 units down, 7 units right

• 4 units left, 7 units right

• 4 units left, 7 units up

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. When does the rock hit the ground?

• 1.094 seconds

• 174.141 seconds

• 155 seconds

• 4.393 seconds

• None of the above

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the maximum height the rock reaches ?

• 1.094 ft

• 174.141 ft

• 155 ft

• 4.393 ft

• None of the above

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. How long does it take the rock to reach its maximum height?

• 1.094 seconds

• 174.141 seconds

• 155 seconds

• 4.393 seconds

• None of the above